Question

1. The response to a question has three alternatives: A, B, and C. A sample of 120 responses provides 60 A, 24 B, and 36 C. Show the frequency and relative frequency distributions. 
2. A questionnaire provides 58 Yes, 42 No, and 20 no-opinion answers. a) In the construction of a pie chart, how many degrees would be in the section of the pie showing the Yes answers? b) How many degrees would be in the section of the pie showing the No answers? c) Construct a pie chart. d) Construct a bar chart. 

Answer 1

1.

$$\def\arraystretch{1.5} \begin{array}{c:c:c} Value & Frequency & Relative\ frequency \\ \hline A & 60 & 0.5 \\ \hdashline B & 24 & 0.2 \\ \hdashline C & 36 & 0.3\\ \hdashline Total & 120 & 1 \\ \end{array}$$

2. How many answers are there?

$$58+42+20=120$$

Suppose the total number of answers correspond to $360\degree$.

Then 1 answer corresponds to $\dfrac{360\degree}{120}=3\degree.$

a)

$$58\cdot3\degree=174\degree$$

In the construction of a pie chart, 174 degrees would be in the section of the pie showing the Yes answers.

b)

$$42\cdot3\degree=126\degree$$

In the construction of a pie chart, 126 degrees would be in the section of the pie showing the No answers.

c)

d)