Maths Quest Maths B Year 11 for Queensland Chapter 10 Summary Statistics Worksheet 10.11

Maths Quest Maths B Year 11 for Queensland Chapter 10 Summary statistics WorkSHEET 10.1 1

WorkSHEET 10.1 Summary statistics Name: ______

1 These data give the amount of weekly pocket 4 money given to a student for 8 weeks:

$5.80, $6.40, $5.00, $6.50, $6.80, $5.90, $6.80, $5.20.

(a) Find the mean of the pocket money. (b) Find the median of the pocket money. (c) Find the mode of the pocket money.

2 This frequency table shows the sick days taken 5 by the workers in a factory in a month.

Number of sick Frequency days (f) 0 8 1 6 2 4 3 2 4 4 5 3 6 3

(a) Find the mean number of sick days per worker. (b) Find the median number of sick days per worker. (c) Find the mode for the number of sick days. Maths Quest Maths B Year 11 for Queensland Chapter 10 Summary statistics WorkSHEET 10.1 2

3 This grouped frequency table shows the area of 5 farm lots in hectares.

Area (ha) Frequency 30- 3 40- 2 50- 8 60- 6 70- 3 80- 1 90- 2

(a) Add the midpoint x, frequency times midpoint f  x and cumulative frequency columns to the table. Write down the sum of f and f  x columns. (b) Find the mean area of the farm lot. (c) Find the median area of the farm. (d) Find the mode.

4 Find the range of each of the following sets of 3 data. (a) 2, 5, 4, 5, 7, 4, 3 (b) 103, 108, 111, 102, 111, 107, 110 (c) 2.5, 2.8, 3.4, 2.7, 2.6, 2.4, 2.9, 2.6, 2.5, 2.8 Maths Quest Maths B Year 11 for Queensland Chapter 10 Summary statistics WorkSHEET 10.1 3

5 Use the frequency distribution tables below to (a) 2 find the range for each of the following sets of scores. (a) Score Frequency 89 12 90 25 91 36 92 34 93 11 94 9 95 4

(b) Class Frequency 150 – 155 12 155 – 160 25 160 – 165 38 165 – 170 47 170 – 175 39 175 – 180 20

6 The number of goals scored by a team is shown 3 below:

5, 4, 4, 7, 5, 9, 12, 14, 16, 16.

(a) Find the lower quartile. (b) Find the upper quartile. (c) Find the interquartile range

7 The stem-and-leaf plot below gives the exact 3 masses of 24 packets of biscuits. Find the interquartile range of the data.

Key: 248 | 4 = 284.4 g

Stem | Leaf 248 | 4 7 8 249 | 2 3 6 6 250 | 0 0 1 1 6 9 9 251 | 1 5 5 5 6 7 252 | 1 5 8 253 | 0 Maths Quest Maths B Year 11 for Queensland Chapter 10 Summary statistics WorkSHEET 10.1 4

8 Use your calculator to find the standard 1 deviation of the set of outcomes when a six-sided die is rolled as shown below.

1, 2, 3, 4, 5, 6

State your answer correct to 2 decimal places.

9 A supermarket chain is analysing its sales over 3 a week. The chain has 15 stores and the sales for each store for the past week were ( in $million):

1.5 2.1 2.4 1.8 1.1 0.8 0.9 1.1 1.4 1.6 2.0 0.7 1.2 1.7 1.3

(a) Calculate the mean sales for the week. (b) Should the population or sample standard deviation be used in this case? (c) What is the value of the appropriate standard deviation?

10 The following frequency distribution gives the 2 prices paid by a car wrecking yard for a sample of 40 car wrecks.

Price ($) Frequency 0 – 500 2 500 – 1000 4 1000 – 1500 8 1500 – 2000 10 2000 – 2500 7 2500 – 3000 6 3000 – 3500 3

Find the mean and standard deviation of the price paid for these wrecks.