Chapter 6 Measures of Central Tendency 6.1
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Chapter 6 Measures of Central Tendency 6.1
Chapter 6 Measures of Central Tendency
WARM-UP EXERCISE 1. The following is the daily average temperatures for the past 30 days (in C). 23 22 24 23 25 26 28 29 30 31 25 26 26 28 31 32 36 33 30 29 29 28 27 28 29 30 25 24 25 28 (a) According to the above data, construct a frequency distribution table by taking 22C - 24C as the class interval of the first class.
(b) Using the frequency distribution table in (a), construct a histogram.
[ A copy of the figure is provided in the Appendix. ] Daily average temperatures for the past 30 days y c n e u q e r F
0
Average temperature (C) 2. The following frequency distribution table shows the Mathematics test scores of the students in a tutorial class. Score Frequency 21 - 30 1 31 - 40 1 41 - 50 5 51 - 60 12 61 - 70 7 71 - 80 6 81 - 90 4 91 - 100 4 Total 40 6.2 New Trend Mathematics S3A — Junior Form Supplementary Exercises
(a) According to the above information, construct a cumulative frequency table. (b) Using the cumulative frequency table in (a), construct a cumulative frequency curve.
[ A copy of the figure is provided in the Appendix. ] Mathematics test scores of the students in a tutorial class y c n e u q e r f
e v i t a l u m u C
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Score
BUILD-UP EXERCISE [ This part provides two extra sets of questions for each exercise in the textbook, namely Elementary Set and Advanced Set. You may choose to complete any ONE set according to your need. ] Exercise 6A Elementary Set Level 1 1. Find the mean of each of the following sets of data. (a) 2, 3, 4, 5, 8, 8 (b) 20, 21, 24, 25, 28, 29, 32, 39, 40, 42
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(c) 10, l 15, 20, 50, 120, 150, 200, 315
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2. Find the mean of each of the following sets of data. (a) 10 000, 100, 150, 200, 250 (b) 45, 56, 40, 42, 9 (c) 0.25, 0.12, 0.23, 0.42, 0.35 Level Level 12 1 1 7 1 0 9 8 6 5 4 3 ...... It is given that the mean of 6 numbers is 13.24. If a datum a If numbers. 7 13.24. these is of numbers 6 of mean the that given is It of mean the If how question minutes, 2.5 choice is multiple question 30 answer choice to take multiple he a does answer long to Kent for required time mean the If time travelling time travelling mean The mean the Find of week. number the shows table following The data. following the of mean the Find 6 of records jump high The oranges? of weight total The glasses. the of price selling mean the find total, in $294 at sold are glasses 7 If Find the mean the Find (b) (a) 2 Number of of Number Find the mean of the data in in data the of mean the Find table. distribution frequency following the Complete 172 4, 4, F Dat
cm, 170 cm, requency 5, 5, um 16 15 14 13 1, 4, 4, 1, journey ( of the of Total 2, 5, 5, 2, x of Kenny to school in 8 days 8 in school to Kenny of
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12.5 Measures of Central Tendency Central of Measures 10 11
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14 12 10.56 is inserted, find the mean the find inserted, is 10.56 x . 50 13 9
passengers by MTR in a in MTR by passengers 14 4 15 2 6. 3 6.4 New Trend Mathematics S3A — Junior Form Supplementary Exercises
13. Candy bought three gifts at a mean price of $95. If she buys one more gift at $102, what is the mean price of these four gifts?
14. It is expected that 32 students will participate the S3A picnic at the fee of $105 each. If 2 students decide not to participate the picnic and their fees are shared among the participants, how much does each participant have to pay for the picnic now?
15. The mean of two numbers is 10 and the mean of another three numbers is 15. (a) Find the sum of these five numbers.
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(b) Hence find the meanl of these five numbers.
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16. (a) Complete the followingy frequency distribution table.
Class Class mark (x) Frequency (f ) fx
26 - 30 3
31 - 35 9
36 - 40 15
41 - 45 8
46 - 50 5 Total
(b) Find the mean of the data in (a).
Advanced Set Level 1 1. Find the mean of each of the following sets of data. (a) 13, 13, 16, 18, 18, 20, 21 (b) 1.03, 1.52, 1.52, 1.61, 1.64 (c) 25, 39, 21, 28, 14, 17, 17 (d) 73.9, 72.8, 43.1, 62.8, 51.9, 63.6 1 5 384 (e) , 2, , 3, 3, 7 (f) 18, 21, 35, 28, 20, 21, 25, 2 2 25
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2. Sammy bought a pack of 300 g of strawberries from a fruit store. If there are
d 15 strawberries in the pack, find the mean weight of the strawberries.
3. There are 8 staff members in a company and their monthly salaries are as follows: $4 000, $6 000, $6 500, $7 500, $7 500, $9 500, $10 500, $2 000 Find the mean of their monthly salaries. Level Level 1 1 1 0 9 8 7 6 5 4 ...... of these 45 these of 30 of mean The family the of charge electricity electricity the mean If the is $432. what was August to $645, May July from was and August June in May, family in the family of a charge of charge electricity mean The complete to athlete 55.2 an for time mean The figures.) significant 3 to answer your (Correct is numbers. 15 numbers these 13 of of mean mean the that given is It of mean the If much students 9 If mean. the calculate and table distribution frequency following the Complete 3 to answers your (Correct data. of sets necessary.) if following figures the of each of mean the Find (c) (b) (a) 2 Dat 2.56, 3.87, 3.87, 2.56, 4,
s to to s 10, 20, 20, 10, is the bill for lunch for bill the is um 40 35 30 25 20 15 10 2, 2, 400 ( complete the 6th time of time 6th the complete Total x numbers. 4, 5, 0, 7, 7, 0, 5, 4,
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numbers is 11.5 and the mean of another 15 another of mean the and 11.5 is numbers 4.15, 4.15,
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8, 8, 5 6.06, 10.05, 10.05, 6.06, ? (Correct your answer to 2 decimal places.) decimal 2 to answer your (Correct ? 25, 25, , 10 10 20 30 15 10 5
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Measures of Central Tendency Central of Measures is 24, find the value of of value the find 24, is equally the mean time for the athlete to athlete the for time mean the 1.4 and 1.9 are inserted are 1.9 and 1.4
numbers is 12.4. Find the mean the Find 12.4. is numbers , each of them pay them of each ,
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$33. How $33. significant , find the find 6. 5 6.6 New Trend Mathematics S3A — Junior Form Supplementary Exercises
12. (a) The following frequency distribution table shows the time spent by a group of people on watching TV last week. Complete the following table.
Time ( hour ) Class mark (x ) Frequency (f ) fx
16 - 20 15
21 - 25 25
26 - 30 30
31 - 35 20
36 - 40 10 Total
(b) Find the mean time in (a).
13. The mean score of 5 tests of Peggy is 45.5. If there is one more test for her and she wishes
to obtain a mean score of 50 for theA 6 tests, what score should she get in the 6th test?
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14. It is known that the mean of the number of push-ups done by S3A boys in a minute is 21; by the S3A girls is 9; and by the whole class is 13.4. If there are 30 students in S3A, find the respective number of boys and girls in the class.
15. The weights of the students in S3A are as follows: Weight (kg) 30 - 34 35 - 39 40 - 44 45 - 49 50 - 54 Frequency 8 12 12 x 2
If their mean weight is 39.75 kg, find the value of x.
16. An exploring team of 10 members crossed a desert. They prepared 900 L of drinking water for a 15-day journey. In the first four days, each member consumed 6 L of drinking water each day on average. On the fifth day morning, 150 L of drinking water was poured out accidentally. For the remaining 11-day journey, how much drinking water, on average, can each member consume each day? (Correct your answer to 3 significant figures.)
Exercise 6B Elementary Set Level 1
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(c) 15, 18, 21, 29, 32, 35, 40, 47, 52, 60, 100 8 7 6 5 4 3 2 ...... h olwn uuaie feuny plgn sos te the shows polygon frequency cumulative following The of number the shows table distribution 50 frequency following The primary 49 of students. money these of pocket money the pocket median shows the Find day. table a in students distribution frequency following The 7.5 of weights respective The data. of sets following the of each of median the Find data. of sets following the of each of median the Find data. of sets following the of each of median the Find ( ( ( ( (b) (a) ( ( ( c b a c b a c ) ) ) ) ) ) )
Pocket money money Pocket people during during people Number of of Number kg 21, 32, 57, 49, 49, 57, 32, 21, 9.8 9.8, 10.2, 10.1, 8.9, 9.5, 9.8, 9.0, 9.0, 9.2, 46 46, 45, 58, 53, 48, 50, 49, 8.2, 2.3, 24 20, 16, 21, 18, 10, 12, 17, 13, 4 7, 1, 9, 5, 2, 8, 36.1 25.4, 19.2, 16.7, 12.8, 11.3, 10.5, 10.2, 36 24, 17, 10, 8, 3, 4, 4, F , , requency 7.2 4, 4,
kg F requency 3, 1, 5, 8 5, 1, 3, , , movies watched movies 4.1, 3.0, 3.0, 4.1, 8.4 ($) a
summer vacation. Find the median number of of number median the Find vacation. summer kg 28, 69, 30, 30, 69, 28, and and 2.9, 2.9, 2 3 7.0 ten pumpkins are 5.4 are pumpkins ten
kg 1.8, 1.8, 5 4 Epumpkins. ten these of xweight median the .Find . 6B Elementary 35, 4 0
Set 0.8, 40, 27 40, Chapter 6 Chapter 10 5 1.4, 0.9 1.4, 8 1 12 6
kg, 6.5 kg, Measures of Central Tendency Central of Measures 12 2 4 7
kg, 4.8 kg, 15 3 nelgne qoin ( quotient intelligence 8 8
movies watched movies kg, 7.2 kg, 8 4 ois wthd by watched movies 5 9
kg, 8.0 kg, 5 or more or 5 3 10 or more or 10
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kg , 6.8 New Trend Mathematics S3A — Junior Form Supplementary Exercises
results of 100 students. Find the median I.Q. test results of the students. I.Q. test results of 100 students
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9. Find the median of the data in the stem- E Stem (10) Leaves (1)
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10. The stem-and-leaf diagram shows the Mathematics test scores of Mathematics test scores of the students in the students in S3A S3A. Stem (10 marks) Leaves (1 mark) (a) How many students are recorded in the stem-and-leaf diagram? 4 4 6 6 6 5 0 1 1 3 8 9 (b) Find the median test score. 6 2 4 7 7 7 8 8 9 9 7 1 1 2 3 3 3 5 5 7 8 9 8 2 8
Level 2
11. Find the median of x 1, x 3, x 5, x 1 and x 2.
12. It is known that the quantity (in glasses) of soya milk sold in the past six days were 121, 103, 106, 110, 106 and 113. (a) Find the median quantity of soya milk sold in the past six days. (b) If 135 glasses of soya milk were sold today, find the median quantity of soya milk sold in these seven days. Level Level 1 1 1 4 3 2 1 5 4 3 ...... mobile phone last week. Find the median number of of number of median the Find number week. last the phone mobile shows table following The 4.9 4.9 are watermelons eight of weights The of median the Find data. of sets following the of each of median the Find t If of value the Find data of set a of median The time spent median time the the shows table following The (d) ( ( (a) ( ( ( (a) c b d c b ) ) ) ) ) 1 Number of of Number he mean of three consecutive numbers is 24 is numbers consecutive three of mean he
kg. Find the median the Find kg. 1.2, 2.4, 2.4, 1.2, 7 8, 9, 4, 8, 6.5, 7, 6, 5, 8, 6, 5.5, 3 14, 12, 20, 4, 5, 10, 1, 4, 7, 9, 32 28, 19, 18, 16, 14, 13, 10, 0 52 41, 30, 25, 21, 20, 18, Time ( Time 1 2 F . 14, 0 14, requency ,
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spent x . each of each 6, 6, . 0.9, 0.9, 5 0 10, 10, weight of these eight watermelons. eight these of weight the following sets of data. of sets following the 4, 9, 12, 13, 13, 12, 9, 4, 2.8, 0.4, 0.4, 2.8, 18 7 1 31 0
Advanced Set Advanced 0.3, 1.4, 2.3 1.4, 0.3, 8 2 Chapter 6 Chapter 22 1 x
kg, 4.6 kg, by 4 by , 16, 20 16, , phone surveys phone 10 3 , f , 0 18
ind the median of these these of median the ind 2 kg, 5.1 kg,
students on using computer in a day. Find day. a in computer using on students and and Measures of Central Tendency Central of Measures phone surveys received surveys phone
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received by 85 people 85 by received Set
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and Elementary Set 9 4 . 6.10 New Trend Mathematics S3A — Junior Form Supplementary Exercises
5. The following cumulative frequency polygon shows the weights of 40 dogs. Find the median weight. Weights of 40 dogs
40
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6. Find the median of the data in the following stem-and-leaf diagram.
Stem (10) Leaves (1)
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7. Find the median of 2x 5, 2x 3, 2x 7, 2x 1, 2x 7 and 2x.
8. The following table shows the number of pairs of sport shoes owned by a group of students. Number of pairs of Frequency sport shoes 1 4 2 21 3 24 4 0 5 1
(a) How many students are recorded in the table? (b) Find the median number of pairs of sport shoes owned by these students. Level Level 1 1 1 1 1 1 5 4 3 2 1 0 9 ...... The following back-to-back stem-and-leaf diagram shows the weights of 30 chicken 30 of weights the shows diagram stem-and-leaf back-to-back following The for breath their following The $12 The following The of mean The numbers. four these of median the Find 17.5. is numbers consecutive four of mean The is order data of set a of median The (b) (a) (b) (a) (b) ( a)
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1 . ) consecutive numbers is 12. Find the median of these these of median the Find 12. is numbers consecutive
less than (s) than less quote 300, $1 300,
800 800 moving service quotes from quotes service moving $102 x . is written is . duration 10, 12, 14, 15, 15, 14, 12, 10, of in the in
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Ex.6B x Advanced .
as $800 as sixth purchase, find the median expenditure expenditure Smedian the find epurchase, sixth t for
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Chapter 6 Chapter holding holding Cumulative frequency Cumulative a cumulative frequency polygon. frequency cumulative a x by mistake by , ,
300, $1 300, x by
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Mrs. Chan at a supermarket are supermarket a at Chan Mrs. 5, 24, 25, 28 25, 24, 5, how long (in second) can second) (in long how 9 ten ten Measures of Central Tendency Central of Measures
200, $1 200, $10 moving among these among , what is the actual median median actual the is what , 3 ,
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11 each $8 ? s . 2, Level 1 Level 6C Exercise 5 4 3 2 1 6...... Find the modal class modal the Find group a that housing mod of the types Find in. different live the students shows of table distribution frequency following The in 1 these children in of children of number number the shows table following The mode the Find mode the Find ( from (b) (a) ( (a) ( (a) 12 c c c Number of children of Number ) ) ) Type of housing of Type 8
1.7, 2.3, 1.6, 1.7, 2.0, 2.3, 2.1, 1.9 2.1, 2.3, 2.0, 1.7, 1.6, 2.3, 1.7, 3 5, 8, 6, 3, 4, 8, 6, 3, 28 26, 26, 25, 21, 21, 20, 20 18, 15, 15, 12, 10, 10, 10, 10, (ii) (i) chicken of weight median the Find chicken of weight median the Find 8 F farm A and B. Aand farm
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13, 0, 0, 13, families. Find the mode mode the Find families. 5 or above or 5 6 Village hous 5, 5, 2 e 9, 9, 13, 13, 5 O thers 1 of the of total Chapter 6 Measures of Central Tendency 6.13
(a) Interval 26 - 30 31 - 35 36 - 40 41 - 45 46 - 50 Frequency 3 10 14 6 5
(b) Interval 1 - 3 4 - 6 7 - 9 10 - 12 13 - 15 16 - 18 Frequency 2 9 19 14 19 14
6. The following bar chart shows the sales volume of five types of fruit juice. Find the mode of the sales volume of fruit juice. The sales volume of five types of fruit juice
50
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7. The following frequency polygon shows the travelling time of 40 students to school. Travelling time of 40 students to school
20
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(a) Given that the class interval of the first class is 11 minutes - 20 minutes, complete the Level Level 10 9 8 6. . . . The following shows the working hours of of hours working the shows following The of the mode the Find shows days. 10 past diagram the in salesman stem-and-leaf following The of mod the sales Find the shows chart pie following The (b) ( B 14 a e ) S a 7.5 9.5 2 8 c a Complete the following table. following the Complete of class modal the Find table. distribution frequency following h S l e a s S Time ( Time l
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Working hours ( x hours ) Frequency
4 x 5 5 x 6 6 x 7 7 x 8 8 x 9 9 x 10 10 x 11 11 x 12 12 x 13
(b) Find the modal class of working hours yesterday.
11. The following cumulative frequency polygon shows the electricity charges for a certain period of N families. Electricity charges for a period of N families
90
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0 300.5 500.5 700.5 900.5 400.5 600.5 800.5 1 000.5 Electricity charge ($) (a) Find the value of N. (b) Given that the class interval of the first class is $301 - $400, construct a frequency distribution table according to the cumulative frequency polygon. (c) Find the modal class of electricity charges. (d) Find the frequency of the modal class obtained in (c).
Advanced Set Level Level 6 5 4 3 2 1 6...... The following shows the shows following The the shows chart 40 pie following The class modal the Find mode sold shop shoe A mode the Find mode the Find (b) (a) ( (b) (a) (b) (a) (c) Q 16 c u )
1 a citizens weekly. citizens F F How many citizens citizens many How weekly. bought magazines of number mode the Find 5 9, 13, 19, 10, 17, 11, 9 5, 3, 3, 0, 8, 0, 14, 8, 0, 149, 154, 150, 149, 162, 149, 150, 12 12, 12, 11, 10, 10, 9, 9, n 1 2 requency requency Interval 4, 4, t s i 0 Size , of of t
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Find the modes of the ages of students started wearing glasses. Ages of 20 students started wearing glasses
10 11 12 13 14 15 Age
7. The following frequency polygon shows the duration of 26 movies. The class interval of the first class is 80 minutes - 89 minutes. Find the modal class of the duration of the movies. The duration of 20 movies
10
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Level 2 8. The following shows the number of subjects with credits for secondary three students in 1 0 9 6. . . The following cumulative frequency table shows the floor areas of the flats of 30 families. 30 of flats the of areas floor the shows table frequency cumulative following The (b) the shows diagram obtain stem-and-leaf following The examination. final (a) (b) (a) 18 S A t (ii) (i) mode the Find subjects of number of mode the Find number of modes respective the Find Floor area less than less area Floor e Number of subjects of Number g m e ed
s ( New Trend Mathematics S3A S3A Mathematics Trend New According to the above stem-and-leaf diagram, complete the following table. following the complete diagram, stem-and-leaf above the to According Find the modal class of age of class modal the Find 1 driving licen driving o 0 1 4 3 2 f )
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50 drivers 50 three three students. when they when Chapter 6 Measures of Central Tendency 6.19
9.5 0 29.5 3 49.5 5 69.5 25 89.5 30
(a) Given that the class interval of the first class is 10 m2 - 29 m2, complete the following table. 2 Floor area (m ) Frequency
10 - 29
30 - 49
50 - 69
70 - 89
(b) Find the modal class of floor areas.
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Exercise 6D Elementary Set Level 1 Level Level 3 5 4 2 1 6...... The following table shows the respective prices of 10 of prices respective the shows table following The 16 of salaries the shows following The thousand ten (in revenues ten the shows table following The a knit to students ten of group a by required hour) (in time the shows following The (b) (a) ( ( ( ( ( (a) ( ( 20 b a b a b b a ) ) ) ) ) ) ) 107 106 $9 $8 2 Price 20 20
months. The following table shows the respective prices and stock of the 10 the of stock and prices respective of the shows table following The with agree you Do $12. of price a at selling are him? items the of most that claims owner The situation? real the reflect can average Which mode and median mean, the Find Why? situation? real the reflect mode the Can data. following the of mode the Find mode and median mean, new the find removed, are revenues. the of revenues lowest and highest the If revenues. the of mode and median mean, the Find require? she does long how scarf, a and knit to mode students the ten than time the of one is Holly If time. the of mode and median mean, the Find Item
000 000 each item is also taken into account into taken also is item each 56 24 95
New Trend Mathematics S3A S3A Mathematics Trend New ($) Item 105 119 23 12 $10 $8 92 81 24 12 A
000 103 115 000 30 24 A 72 84 24 25 B 104 236 $6 $7 28 21 B
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Ex.6D Elementary Set Level Level Level 4 3 2 1 . . . . Mr. Chan Chan Mr. (a) between the shows table following The shop average toy the of owner to According ha students that month) (in time the shows following The ( (b) ( ( c b a ) shots hitting shots ) ) 42 000 42 000 34 2 1 12 10 Number of Number the target the In this match, which average (mean, median and mode) reflects the reality better? in reality the leading reflects mode) is and median Who (mean, wins. average which target match, the this In hitting shots more with rounds the of most player the round, each In (ii) (i) reflect to suitable most is average Which time. learning of mode and median mean, the Find Price ($) Price Stock id te en mda ad md mode and Mr. median mean, the Find mode and Mr. median mean, the Find Mr. Chan and Mr. Lee. Mr. and Chan Mr. did he possibly use to support his statement his support to use possibly he did is going is 11 11 Round
Lee. Chan 43 000 43 000 45 the monthly net profits (in profits net monthly the Mr. Chan Mr. . Mr. Lee Mr. 15 15 to buy four kinds of wallpapers wallpapers of kinds four buy to 270 12
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34 000 34 000 27 d e c n a v d 14 A 12
35 25 D 6 . x E 3 5 1 number 10 13 15 30
31 000 31 30 000 30 Advanced Set Advanced 7 6 2 of of Chapter 6 Chapter 14 9
250 12 )o of $) shots hitting the target in in target the hitting shots s f of f h nme o ht htig te agt by targets the hitting shots of number the of the the 3 2 3 33 000 33 30 000 30 12 16 the the number of shots hitting the targets by targets the hitting shots of number the Ex.6D real situation of learning time? learning of situation real 120
Advanced 18 Measures of Central Tendency Central of Measures toy shop last year last shop toy from Set ?
2 7 4 13 9 a store. The following table shows table following The store. a 380 ve 12 35 000 35 46 000 46 learned piano in a piano class. piano a in piano learned
8 1 5 15 12 60 20 each round round each 10 13 6 4 6 as shown below, shown as 80 20 5 5 7 42 24 of a match a
6. W 1 4 8 21 28 26 hich the Level 1 Level 6E Exercise
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Mr. Chan buy the wallpaper at at wallpaper the buy Chan Mr. m 17 kg,
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subtracted from from subtracted kg 26 and and
m Mr. Chan accept the special offer? special the accept Chan Mr. L. 18 each datum each Marked price per roll per price Marked
better reflect better kg . ce of of ce $680 $600 A each datum each Ex.6E $33 $35 $52 $60 does the manufacturer come to this conclusion this to come manufacturer the does there is no change in change no is there , find the new mean, median and mode. and median mean, new the find ,
Elementary the
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y 4. It is known that the median of a set of data is 8. If x is added to each datum, the new median becomes 15. Find the value of x.
5. For a set of data, the mode becomes 21 after subtracting 3 from each datum. Find the original mode.
6. A set of data 102, 148, 129, 113, 120, 119, 118, 115, 117, 119, 110, 118, 115, 118 and 117 is given. (a) Find the median of this set of data. (b) If the data ‘119’ and ‘120’ are inserted, find the new median. (c) If a datum ‘148’ is removed, find the new median.
Level 2 7. It is known that the mean of a set of 10 data is 24. (a) Find the sum of this set of data. (b) If the data ‘28’ and ‘34’ are removed, (i) find the sum of the remaining data. (ii) find the new mean.
8. A set of data 0.5C, 0.2C, 0C, 0.1C, 0.6C, 1.2C, 1.5C and 1.5C is given. (a) Find the mode of this set of data. (b) If each datum is multiplied by x, the new mode is 0.3C. Find the value of x.
9. A set of data 10, 11, 12, 13 and 14 is given. (a) Find the mean of this set of data. (b) If a new datum ‘0’ is inserted, find the new mean. (c) If a datum ‘x’ is removed, the new mean is 12.5. Find the value of x.
10. A test paper consists of 20 multiple choices questions with equal score. It is known that the mean score of S3A students is 28 and the mean of the number of their correct answers is 14. (a) Find the score of each question. (b) If the median of the number of correct answers is 16, find the median score of the students. (c) If the mode of the scores of the students is 34, find the mode of the number of correct answers. Level Level Level 7 6 5 4 3 2 1 6...... given. 32 data of set A 25 mean. of new set a of mean the that known is It 18 and 20 20.5, are data of set a of mode and median mode? and median mean, the that respectively. known is It data of set A after 10.5 becomes median the median. original data, of set a For data of table. set a following of mode and median mean, the If given. data of set A (c) (b) (a) (b) ( (c) (b) (a) 24 a ) 2 1 Each datum is datum Each If If data. of set this of mode the Find ‘ datum the If mode new the find inserted, is ‘15’ datum a If data. of set this of mode the Find If 10 If mode and median mean, the Find Each datum is datum Each x is datum each
Each datum Each New Trend Mathematics S3A S3A Mathematics Trend New cm is added to to added is cm Each datum Each
cm is added to to added is cm 12, 13, 14, 14, 14, 15, 15 15, 14, 14, 14, 13, 12, fIf 9
cm
each datum is datum each cm, 35 cm, multiplied by 3 by multiplied divided by 2 by divided x
, 10 , ’ is removed, the new modes are 14 and 15. Find the value of of value the Find 15. and 14 are modes new the removed, ’is minus 4 minus
plus multiplied by 10, 10, by multiplied
cm each datum each
5 cm, 36 cm, each datum each , , 11
multiplied by 2 and then minus 5, what are the new mean, new the are what 5, minus then and 2 by multiplied cm
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, find the new mean, median and mode and median mean, new the find , Advanced Set Advanced s
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cm cm is cm is Level 1 Level 6F Exercise 1 2 1 3 0 9 8 ...... The following table shows a set of data and the corresponding weighting factors. Find the Find factors. weighting corresponding data. the of set and this of data mean of set weighted a shows table following The cloths, the of washing lengths After the of mode and median The 27.5 of set a of mean The data of set A ( (c) (b) (a) (b) (a) ( (a) (b) b a ) ) Weighting factor Weighting Find the weighted mean of the set of data in in data of set the of mean weighted the Find corresponding the and data the of product table. the following the and Complete data factors. of weighting set a shows following The in given data the of mean weighted the Find factors. weighting corresponding the and data of set a table. following the shows Complete table following The of the of length mean the If of lengths the of mode and median the Find datum a If median. new the find inserted, is ‘0’ datum new a If the Find . Find the value of of value the Find . these rolls these Weighting factor Weighting factor Weighting Dat um Dat Dat median of this set of data. of set this of median 13, 14, 16, 20 and 20 and 20 16, 14, 13, ‘ um um um xy xy x ’ is removed, the new median is 18. Find the the Find 18. is median new the removed, ’is of cloth of
( ( x x ) ) 25
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Elementary Set Elementary . If two data ‘ data two If . of cloth of shrink 99 33 55 Chapter 6 Chapter 4 10 6 rolls
(Correct your answer to 3 to answer your (Correct by 1.5%. 1.5%. by s of cloths are are cloths of after washing is 3.2 is washing after 76 38 60 2 20
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x Tendency Central of Measures
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m s and
after washing. after m, find the find m,
significant figures.) significant value 3.05 Ex.6F Elementary s
of of Set m respectively.
mean length mean x . 6. 25 Level Level Level 1 7 6 5 4 6...... The following table shows the sales of five five of of sales number the the shows table following The the If factors. weighting corresponding the and of data value of the find set 6.95, is a mean weighted shows table following The Chinese in Bonnie and Ricky of scores the Language shows table following The figures.) significant 3 to answer your (Correct flowers. of dozen quantity the Using respective the and flowers of kinds three Flower of Beauty by cost purchased the shows table following The (a) integer.) nearest the to answers your (Correct (b) (a) 26 1 2 Number of of Number Weighting factor Weighting factor Weighting Complete the following table. following the Complete January. 5 of sales actual the If sales of number the Using Quantity purchased Quantity Weighting factor Weighting New Trend Mathematics S3A S3A Mathematics Trend New Subject Bonnie Dat Ricky Cost Cost in January in Sales ($) Sales and Mathematics examinations. Who perform Who examinations. Mathematics and Store um Dat employees per employees in each store each in employees um um xy dozen ($) dozen ( x purchased as the weighting factors weighting the as purchased . ) (
( in y )
dozen) 2 employees 8 Chinese th b
store S 280 000 280 hop. 20 5 6 1
Ex.6F 60 80 Language 3 is $350 is A2 dvan9 ced
as Set Advanced Set Advanced — . the 63 21
250 000 250 Junior Form Form Junior Lily b 20 75 3 7 . 000, find the actual weighted mean of the sales in sales the of mean weighted actual the find 000, weighting factors, find the weighted mean of the of mean weighted the find factors, weighting 8 2 stores 22.5 3 English 4 6 of a fashion store chain in January and January in chain store fashion a of 300 000 300
S 24.5 Rose 8 3 upplementary Exercises upplementary Language 75 68 98 5 25 64 ed , f , b 3 better? ind the weighted mean cost of a of cost mean weighted the ind
270 000 270 7 4 Sunflower 10 80 Language Mathematics 280 000 280 9 5 80 72 2 quantities , English , Chapter 6 Measures of Central Tendency 6.27
(b) Find the weighted mean of the data in (a).
2. The following table shows the ratings and their corresponding weighting factors of a light bulb in three different areas. Find the weighted mean of the ratings of the light bulb. Area Brightness Price Lifetime Rating 4 2 3 Weighting factor 8 1 1
3. The following table shows the ratings of Felix in five areas assessed by a recruitment agency. Area Education Experience Language Communication Creativity Rating 6 5 8 5 6
(a) A fashion design company wants to employ a fashion designer through this recruitment agency. The company assesses the performance of a candidate according to the weighting factors as shown in the following table. Find the weighted mean of the ratings of Felix. (Correct your answer to 2 decimal places.) Interview item Education Experience Language Communication Creativity Weighting factor 6 7 5 4 8
A
d
E
v
S (b) A fashion magazine publisher wants to employ x an editor through this recruitment
a
.
e
n
6
t
c
agency. The publisher assesses the performanceF of a candidate according to the
e
weighting factors as shown in the following table.d Find the weighted mean of the
ratings of Felix. (Correct your answer to 2 decimal places.) Interview item Education Experience Language Communication Creativity Weighting factor 8 3 8 6 5
Level 2 4. The following table shows the examination results of Jason and Mandy in the first term. Subject English Chinese Mathematics Science History Art Music Language Language Jason 50 60 55 35 47 68 80 Mandy 60 45 50 70 61 42 53
Miss Lee thinks that the weighting factors of Art and Music should be the same. The weighting factors of Science and History should be 2 times that of Art, and the weighting factors of English Language, Chinese Language and Mathematics should be 3 times that of Art. (a) Write down the weighting factor of each subject. (b) Who has a better overall performance?
5. Three students each from S3A, S3B and S3C participate in a Mathematics quiz. The 6.28 New Trend Mathematics S3A — Junior Form Supplementary Exercises
weighted mean score of three students of each class represents the score of their class in the quiz. The following table shows the scores and the corresponding weighting factors of each student. Find the rankings of the three classes in the quiz. S3A S3B S3C Weighting factor
1st student 80 90 70 3 2nd student 60 80 66 2 3rd student 40 60 63 1
6. The following table shows a set of data and the corresponding weighting factors. If the weighted mean is 59.9, find the value of a. Datum 50 52 60 74 36 80 55 Weighting factor 5 6 4 8 a 3 1
7. The following table shows the profits of Toy City from the sales of six kinds of toy cars and their corresponding sales volumes. Toy car 1 2 3 4 5 6 Profit ($) 10 15 23 26 30 30 Sales volume 13 10 10 4 1 2
(a) Using the sales volumes as the weighting factors, find the weighted mean of the profit from the sales of toy cars. (b) If one more toy car of each kind is sold, what is the new weighted mean? (Correct your answer to 3 significant figures.) (c) If the sales volumes of toy car 4 and toy car 5 were swapped by mistake, find the actual weighted mean profit.
CHAPTER TEST (Time allowed: 1 hour)
Section A (1) [ 3 marks each ] 1. The following table shows the number of times for S3A students dining out last week. Find the mean of the number of times for dining out. (Correct your answer to 3 significant figures.) Number of times 0 1 2 3 4 5 6 7 Frequency 16 10 3 1 2 1 1 1 Chapter 6 Measures of Central Tendency 6.29
2. The following shows the number of fouls of a NBA player in his last ten games. 1 1 3 2 2 4 2 3 1 3 Find the median of the number of fouls.
3. In the figure, find the median height. y
c 50 n e
u 40 q e r f
e 30 v i t a l
u 20 m u
C 10
0 160 165 170 175 180 185 Height (cm) 4. A restaurant provides five choices of set meals for customers. The following shows the orders from 20 customers. Set A Set C Set C Set D Set B Set C Set D Set D Set A Set E Set B Set B Set E Set C Set B Set E Set C Set A Set A Set A Find the modes of the set meals ordered.
5. The histogram shows the distribution of the Lengths of 100 wires lengths of 100 wires. Given that the class interval of the first class is 11 cm - 20 cm, 30 find the modal class of the lengths. 25 y c
n 20 e u q e
r 15 F 10
5
0 15.5 35.5 55.5 25.5 45.5 Length (cm) 6. If each datum of a set increases by 10 and it is then divided by 2, the new mean, median and mode are 30, 32 and 31 respectively. Find the original mean, median and mode of the set of data.
Section A (2) [ 6 marks each ] 7. The following tables show the monthly income of 60 families each in villages A and B. 6.30 New Trend Mathematics S3A — Junior Form Supplementary Exercises
Village A
Monthly Income ($) 1 - 5 000 5 001 - 10 000 10 001 - 15 000 15 001 - 20 000 20 001 - 25 000 Frequency 6 15 25 10 4
Village B
Monthly Income ($) 1 - 5 000 5 001 - 10 000 10 001 - 15 000 15 001 - 20 000 20 001 - 25 000 Frequency 8 18 20 9 5
(a) Find the respective means and modal classes of monthly income in village A and village B. (b) Which village has a higher average monthly income?
8. (a) If the mean of x, 18, 24, x 7, x 9 and 32 is 23.5, find the value of x. (b) Find the median and mode of the set of data.
9. It is known that the mean and mode of 41 data are 25. If the datum ‘12’ is removed, find (a) the new mean. (b) the new mode.
10. The weighted mean of the data in the following table is 112.8, find the value of a. Datum 80 100 120 140 160 Weighting factor 6 7 5 4 a
Section B 11. There are 10 families each in village A and village B. The following tables show the number of members in each family and their corresponding water consumption last year. Village A
Water consumption 402 312 278 315 411 368 327 290 324 356 Number of members 3 3 2 4 3 2 3 4 4 3
Village B
Water consumption 423 415 324 398 402 453 452 390 450 317 Chapter 6 Measures of Central Tendency 6.31
Number of members 5 4 3 4 4 5 4 3 4 3
The means of water consumption of each family in village A and village B are 338.3 m3 and 402.4 m3 respectively. Therefore, residents of village A blame residents of village B for using too much water. (a) Is the method used in arriving the above results reasonable? Explain briefly. (6 marks) (b) Using which method to obtain the average is considered more reasonable? Which of the villages has a higher average water consumption? (7 marks)
Multiple Choice Questions [ 3 marks each ] 12. Find the mean of 4, 7, 3, 0 and 5. ordered by a group of students. Find the A. 3.8 mode of the sizes. Size Frequency B. 4 30 4 C. 4.5 32 11 D. 4.75 □ 34 15 36 16 38 5 13. If the mean of 3, 5 and x is 3, find the value of x. A. 15 A. 1 B. 16 B. 3 C. 34 C. 5 D. 36 □ D. 7 □ 17. If the median of 83, 100, 52, 70, 60 and x is 72.5, then x
14. Find the median of 29, 27, 18, 23, 11 and A. 70. 30. B. 72.5. A. 18 C. 75. B. 20.5 D. 77.5. □ C. 23 D. 25 □ 15. Find the mode(s) of 1, 3, 4, 3, 5, 4, 6 and 18. If the mean of 8, 6, 6, 6, 7, 4, 10, 9, 9 and 7. a is 7, find the median of the ten numbers. A. 1 A. 6.5 B. 3 B. 6 C. 4 C. 5.5 D. 3 and 4 □ D. 5 □
16. The following table shows the distribution of the sizes of sportswear 6.32 New Trend Mathematics S3A — Junior Form Supplementary Exercises
19. Given a set of data x, x 2, x 3, x and III. Mode x 10, which of the following must be A. I only correct? B. II only I. The median is x 3. C. I and II only II. The mean is x 1. D. II and III only III. The mode is 2. □ A. I only B. II only 23. The following table shows the test scores C. I and II only of a student in different subjects and the corresponding weighting factors. Find the D. II and III only □ weighted mean of the scores. Subject Score Weighting factor English 72 5 20. Given a set of data 30, 30, 40, 20, 45, 50 Language and 60, which of the following must be Chinese 60 5 correct? Language A. Mean Median Mode Mathematics 80 3 B. Mean Median Mode Science 90 2 C. Mode Mean Median A. 72 D. Median Mode Mean □ B. 75.5 C. 76 D. 80.5 □
21. A set of data 69, 54, 50, 69 and 45 is given. If a datum ‘54’ is inserted, which 24. It is known that the median of five data is of the following remain(s) unchanged? 11.2. If each datum increases by 10, find the new median. I. Mean A. 10.2 II. Median III. Mode B. 15.2 A. I only C. 21.2 B. II only D. 22.2 □ C. I and II only D. II and III only □ 25. The mean, median and mode of 20 data are 15. If the datum ‘25’ is removed, which of the following must be correct? I. The new mean decreases. 22. Which of the following is/are not II. The median remains unchanged. affected by the extreme data? III. The mode remains unchanged. I. Mean II. Median Chapter 6 Measures of Central Tendency 6.33
A. I only median is x, the median of a, b, c, d, e and x is B. II only A. b. C. I and III only B. d. D. I, II and III □ C. x. c d D. . □ 2 26. If a, b, c, d and e are a set of data arranged in ascending order and the