Chapter 10, Problem 27SGR

a.

To determine

A two way frequency table for the survey

Explanation of Solution

Given information:

A survey was taken asking whether anyone is interested in starting an environmental club.

Of the $28$ boys that responded, $8$ said yes. Of the $34$ girls that responded, $15$ said no.

Calculations:

Here a two way frequency table taking the data of the survey.

Out of $28$ boys, no of boys that rejected is $(28-8)=20$

Out of $34$ girls, no of girls that said yes is $(34-15)=19$

Two way frequency table is shown below.

Activity	Boys	Girls	Total
Interested students	8	19	27
Not interested students	20	15	35
Total	28	34	62

b.

To determine

A relative frequency table by converting the two way frequency table for the survey

Explanation of Solution

Given information:

A survey was taken asking whether anyone is interested in starting an environmental club.

Of the $28$ boys that responded, $8$ said yes. Of the $34$ girls that responded, $15$ said no.

Calculations:

Here a two way frequency table taking the data of the survey.

Out of $28$ boys, no of boys that rejected is $(28-8)=20$

Out of $34$ girls, no of girls that said yes is $(34-15)=19$

Two way frequency table is shown below.

Activity	Boys	Girls	Total
Interested students	8	19	27
Not interested students	20	15	35
Total	28	34	62

Percentage of total number of boys that are interested is

  $\frac{8}{62}\times 100=12.9\mathrm{\%}$

Percentage of total number of boys that are not interested is

  $\frac{20}{62}\times 100=32.25\mathrm{\%}$

Percentage of total number of girls that are interested is

  $\frac{19}{62}\times 100=30.645\mathrm{\%}$

Percentage of total number of girls that are not interested is

  $\frac{15}{62}\times 100=24.19\mathrm{\%}$

Percentage of total interested students is

  $\frac{27}{62}\times 100=43.55\mathrm{\%}$

Percentage of total not interested students is

  $\frac{35}{62}\times 100=56.45\mathrm{\%}$

Now the relative frequency table is,

Activity	Boys	Girls	Total
Interested students	$12.9\mathrm{\%}$	$30.645\mathrm{\%}$	$43.55\mathrm{\%}$
Not interested students	$32.25\mathrm{\%}$	$24.19\mathrm{\%}$	$56.45\mathrm{\%}$
Total	$45.16\mathrm{\%}$	$54.84\mathrm{\%}$	$100\mathrm{\%}$