Question

chapter 2: graphical representations 111
build your skills

1. the circle graph below shows the results of a student survey: 171 students were

asked their favourite colour.
favourite colours
4% 2%
11%
25%
12%
17%
14%
15%
blue
purple
pink
green
red
orange
black
white
0.14×360 = 50.4
0.25×360 = 90
a) how many students chose green as their favourite colour?
b) what is the most popular colour? approximately how many students chose it?

1. the circle graph below indicates the percentage of his income that frank spends on

different items.
expenditures
8%
10%
45%
10%
12%
15%
transportation
savings
entertainment
food
clothing
housing
a) on what two items does he spend the same amount?
saving and entertainment

Explanation:

Problem 1a

Step1: Identify percentage for green

From the pie chart, green is 14% of 171 students.

Step2: Calculate number of students

Number of students = \( 171 \times 0.14 \)
\( 171 \times 0.14 = 23.94 \approx 24 \) (rounded to nearest whole number)

Step1: Identify most popular color

The largest percentage in the pie chart is 25% for blue.

Step2: Calculate number of students

Number of students = \( 171 \times 0.25 \)
\( 171 \times 0.25 = 42.75 \approx 43 \)

Looking at the pie chart for Frank's expenditures, both Savings and Entertainment have a percentage of 10%. So he spends the same amount on Savings and Entertainment.

Answer:

Approximately 24 students chose green.

Problem 1b