Lesson 16.5 Measures of Central Tendency and Grouped Data

NAME: INTEGRATED ALGEBRA 1 DATE: MR. THOMPSON

LESSON 16.5 MEASURES OF CENTRAL TENDENCY AND GROUPED DATA

HOMEWORK ASSIGNMENT # 126: PAGES 695-697: # 2 - 12 EVENS

EXAMPLE I OiliflitEMIZZEITIOMMESEMZESEM72ra, In the table, the data indicate the heights, in inches, of 17 basketball players. For these data find: a. the mode b. the median c. the mean 77 2 Solution a. The greatest frequency, 5, occurs for the height 76 0 of 75 inches. The mode, or height appearing most often, is 75. 75 5 74 3 b.For 17 players, the median is the 9th number, so there are 8 heights greater than or equal to the 73 4 median and 8 heights less than or equal to the 72 2 median. Counting the frequencies going down, 1 we have 2 + 0 + 5 = 7. Since the frequency of 71 the next interval is 3, the 8th, 9th, and 10th heights are in this interval, 74. Counting the frequencies going up, we have 1 + 2 + 4 = 7. Again, the frequency of the next interval is 3, and the 8th, 9th, and 10th heights are in this interval. The 9th height, the median, is 74.

c.(1) Multiply each height by its corresponding frequency: 77 x 2 = 154 76 x 0 = 0 75 x 5 375 74 x 3 = 222 73 X 4 = 292 72 X 2 = 144 71 x 1 = 71 (2) Fmd the total of these products: 154 + 0 + 375 + 222 + 292 + 144 + 71 = 1,258 (3) Divide this total, 1,258, by the total frequency, 17 to obtain the mean: 1258 +47 = 74 14. For which set of data is there more than one mode? (1) 8, 7, 7, 8, 7 (3) 8, 7, 5, 7, 6, 5 (2) 8, 7, 4, 5, 6 (4) 1, 2, 2, 3, 3, 3

16. For which set of data will the mean, median, and mode all be equal? (1) 1, 2, 5, 5, 7 (3) 1, 1, 1, 2, 5 (2) 1, 2, 5, 5, 8, 9 (4) 1, 1, 2

20. Three consecutive even integers can be represented by x, x + 2, and x + 4. The average of these consecutive even integers is 20. Find the integers.

English tests. What grade must she obtain 26. Rosemary has grades of 90, 90, 92, and 78 on foin . on the next test so that her average for the five tests will be 90? Calculator Clear any previous data that may be stored in L1 and L2. Enter the heights of Solution the players into L1 and the frequencies into L2. Then use 1-Var Stats from the STAT CALC menu to display information about the data. The screen will show the mean, T. Press the down arrow key to display the median.

ENTER: All 1M ENTER rfni) UThrid L2 cklid179)

DISPLAY: 1-VAR SUITS 1-11LIR SIM'S 14 .tri.11 x=12 58 !ffiriX=11 x2=93136 Qi.13 5x-1.65831239S fleo.14 0=1.608199333 03=15 l'IsxX=11

Answers a. mode = 75 b. median = 74 c. mean = 74

Writing About Mathematics

1. The median for a set of 50 data values is the average of the 25th and 26th data values when the data is in numerical order. What must be true if the median is equal to one of the data values? Explain your answer.

Developing Skills In 3-5, the data are grouped in each table in intervals of length 1. 01. the mode Find: a. the total frequency b. the mean c. the median

3. uv.24.vat;fl Er,LPAR5-M. I0 9 2 8 3 7 3 - 6 4 $ 3 5. ., !)10.64.1, Frecjüenjfi 25 4 24 23 3 22 2 21 4 20 5 19 2

In 6-8, the data are grouped in each table in intervals other than length 1. Fmd: a. the total frequency b. the interval that contains the median c. the modal interval

4-9 12 10-15 13 16-21 9 22-27 12 28-33 15 34-39 10

Applying Skills 9. On a test consisting of 20 questions, 15 students received the following scores: 17, 14, 16, 18, 17, 19, 15, 15, 16, 13, 17, 12, 18, 16,17 a. Make a frequency table for these students listing scores from 12 to 20.

b. Find the median score.

c. Find the mode.

d. Find the mean. 11. A storeowner kept a tally of the sizes of suits purchased in the store, as shown in the table. a. For this set of data, find: (1) the total frequency riattecii mlorAvensmie:.- .,. kyms.)951ts 48 46 44 3 42 5 (2) the mean 40 3 38 8 36 2 34 2

(3) the median

(4) the mode

b. Which measure of central tendency should the storeowner use to describe the average suit sold? 13. The following data consist of the weights, in pounds, of 35 adults: 176, 154, 161, 125, 138, 142, 108, 115, 187, 158, 168, 162 135, 120, 134, 190, 195, 117, 142, 133, 138, 151, 150, 168 172, 115, 148, 112, 123, 137, 186, 171, 166, 166, 179

a. Organize the data in a table, using 100-119 as the smallest interval.

b. Construct a frequency histogram based on the grouped data.

d. What is the modal interval? c. In what interval is the median for these grouped data? NAME: INTEGRATED ALGEBRA 1 DATE: MR. THOMPSON

HOMEWORK - LESSON 16.5 MEASURES OF CENTRAL TENDENCY AND GROUPED DATA

HOMEWORK ASSIGNMENT # 126: PAGES 695-697: # 2 - 12 EVENS

Writing About Mathematics

2. What must be true about a set of data if the median is not one of the data values? Explain your answer.

Developing Skills In 3-5, the data are grouped in each table in intervals of length 1. Fmd: a. the total frequency b. the mean c. the median d. the mode

.: 15 3 16 2 17 4 18 1 19 5 20 6

In 6-8, the data are grouped in each table in intervals other than length 1. Fmd: a. the total frequency b. the interval that contains the median c. the modal interval 6.

55-64 3 45-54 35-44 7 25-34 6 15-24 2 !;=.,7;i3041,4triAT4;` 8. AnterealiA .reque,A, 126-150 4 101-125 6 76-100 6 51-75 3 26-50 7 1-25 2

Applying Skills

10. A questionnaire was distributed to 100 people. The table shows the time taken, in minutes, to complete the questionnaire. a. For this set of data, find: (1) the mean (2) the n 0....., `,:tEcequencyt median (3) the mode 6 12 5 20 4 36 3 20 2 12

b. How are the three measures found in part a related for these data?

12. Test scores for a class of 20 students are as follows: 93, 84, 97, 98, 100, 78, 86, 100, 85, 92, 72, 55, 91, 90, 75, 94, 83, 60, 81, 95 a. Orgsnin the data in a table using 51-60 as the smallest interval.

b. Find the modal interval.

c. Find the interval that contains the median.