Question

A whatjapanthinks.com survey asked residents of Japan to name their favorite pizza topping. The possible responses included the following choices: pig-based meats, for example, bacon or ham (PI); seafood, for example, tuna, crab, or cod roe (S); vegetables and fruits (V); poultry (PO); beef (B); and cheese (C). The following data represent the responses of a random sample of 36 people.
V PI B PI V PO S PI V S V S
PI S V V V PI S S V PI C V
V V C V S PO V PI S PI PO PI
a. Prepare a frequency distribution table.
b. Calculate the relative frequencies and percentages for all categories.
c. What percentage of the respondents mentioned vegetables and fruits, poultry, or cheese?
d. Draw a bar graph for the relative frequency distribution.

Answer 1

Answer:

See Explanation

Step-by-step explanation:

Solving (a):

First, we categorize each data (to get their frequencies):

PI PI PI PI PI PI PI PI PI ---> Frequency: 9

S S S S S S S S---> Frequency: 8

V V V V V V V V V V V V  V ---> Frequency: 13

PO PO PO---> Frequency: 3

B ---> Frequency: 1

C  C ---> Frequency: 2

Total = 36.

The frequency table is as follows:

$\begin{array}{cc}{Pizza\ Topping} & {Frequency} & {Beacon\ or\ Ham} & {9} & {Seafood} & {8} \ \\ {Vegetable\ and Fruit} & {13} & {Poultry} & {3} & {Beef} & {1} & {Cheese} & {2}\ \end{array}$

Solving (b): The relative frequency and percentage.

Relative frequency is calculated by dividing each frequency by the total frequency.

So, we have:

${Beacon\ or\ Ham} = \frac{9}{36} =0.250$

$Seafood = \frac{8}{36} =0.222$

$Fruits\ and\ Vegetable = \frac{13}{36}=0.361$

$Poultry = \frac{3}{36}=0.083$

$Beef = \frac{1}{36}=0.028$

$Cheese = \frac{2}{36}=0.056$

The percentage is calculated by multiplying the frequency by 100%.

So, we have:

$Bacon\ or\ Ham = 0.250 * 100\% = 25.0\%$

$Seafood = 0.222 * 100\% = 22.2\%$

$Fruits\ and\ Vegetable= 0.361 * 100\% = 36.1\%$

$Poultry = 0.083 * 100\% = 8.3\%$

$Beef = 0.028 * 100\% = 2.8\%$

$Cheese = 0.056 * 100\% = 5.6\%$

Solving (c): Percentage that mentioned vegetables and fruits, poultry, or cheese?.

This is calculated as:

$\%Percent = Vegetable\ and\ fruits + Poultry + Cheese$

$\%Percent = 36.1\% + 8.3\% + 5.6\%$

$\%Percent = 50\%$

(d) See attachment for bar graph