Question

Use the data collected from a class about their feelings toward math to complete the table needed to create a pie chart. Round the percentages to one decimal place, and the degrees to the nearest whole number.

Answer 1

Table shown below

Explanation:

Statistics Tables

The data collected from field measures is usually shown in logically ordered tables where the numbers are prepared to further elaborate different types of graphs, like the pie charts who need to compute the angle of each frequency.

The percentage of each frequency is computed as

`\displaystyle pct_i=(x_i)/(n)*100%`

Where
`x_i` is the frequency of the option i and n is the sum of the frequencies

The angles of each frequency is computed as

`\displaystyle angle_i=(x_i)/(n)*360^o`

Let's fill out all the spaces left in the table. We first need to compute the value of n

n=2+6+12+5+3=28

The filled spaces are shown in red

Now let's compute all the percentages

The "Love it" option:

`\displaystyle pct_i=(2)/(28)*100\%=7.1\%`

The "Like it" option (to verify):

`\displaystyle pct_i=(6)/(28)*100\%=21.4\%`

as already shown.

The "Take or leave" option:

`\displaystyle pct_i=(12)/(28)*100\%=42.9\%`

The "Don't like" option:

`\displaystyle pct_i=(5)/(28)*100\%=17.9\%`

The "Hate it" option (verifying):

`\displaystyle pct_i=(3)/(28)*100\%=10.7\%`

The sum of percentages is 100% as expected

Now for the angles

The "Love it" option:

`\displaystyle angle_i=(2)/(28)*360^o=26^o`

The "Like it" option:

`\displaystyle angle_i=(6)/(28)*360^o=77^o`

The "Take or leave" option:

`\displaystyle angle_i=(12)/(28)*360^o=154^o`

The "Don't like" option:

`\displaystyle angle_i=(5)/(28)*360^o=64^o`

The "Hate it" option:

`\displaystyle angle_i=(3)/(28)*360^o=39^o`

The sum of the angles is 360°