Question

1. a sample of university employees are surveyed about their primary method of commuting to work. the results of this survey are presented in the table below. if we use this table of data to construct a pie chart, which one of the following statements most accurately depicts what this pie chart would look like?

commuting method	number of employees
bus	101
train	79
bicycle	49
walking	20

a. the slice for \car\ would encompass exactly half of the pie chart.
b. the slice for \walking\ would be about 5% of the pie chart, making it the smallest slice.
c. the slice for \bicycle\ represents one - tenth of the pie chart.
d. the combined slices for \bus\ and \train\ would take up a little more than one - third of the pie chart.
e. it would be impossible to construct a pie chart to graph this data because the categories are not numerical.

Explanation:

Step1: Calculate total number of employees

$248 + 101+79 + 49+20=497$

Step2: Analyze option A

The proportion of car - commuting employees is $\frac{248}{497}\approx0.499
eq0.5$, so option A is incorrect.

Step3: Analyze option B

The proportion of walking - commuting employees is $\frac{20}{497}\approx0.0402\approx4\% \approx 5\%$, and 20 is the smallest number among the categories, so this option is correct.

Step4: Analyze option C

The proportion of bicycle - commuting employees is $\frac{49}{497}\approx0.0986
eq0.1$, so option C is incorrect.

Step5: Analyze option D

The combined number of bus and train - commuting employees is $101 + 79=180$. The proportion is $\frac{180}{497}\approx0.362\lt\frac{1}{3}\approx0.333$, so option D is incorrect.

Step6: Analyze option E

Pie charts can be constructed for non - numerical categories with numerical frequencies, so option E is incorrect.

Answer:

B. The slice for “Walking” would be about 5% of the pie chart, making it the smallest slice.