Question

1. christy surveyed several students at her school and asked each person which foreign language he or she is studying. the results are shown in the table.

	male	female	total
french	16	12	28
german	6	8	14
total	40	40	80

construct a relative - frequency table by converting the data in the table to percentages. round to the nearest tenth if necessary.

find the joint relative frequency of a female student who is studying french.

make two observations.

Explanation:

Step1: Calculate relative - frequency for each cell

To find the relative - frequency of a cell, divide the value in the cell by the total number of students (80).
For male Spanish students: $\frac{18}{80}=0.225 = 22.5\%$
For female Spanish students: $\frac{20}{80}=0.25 = 25\%$
For male French students: $\frac{16}{80}=0.2 = 20\%$
For female French students: $\frac{12}{80}=0.15 = 15\%$
For male German students: $\frac{6}{80}=0.075 = 7.5\%$
For female German students: $\frac{8}{80}=0.1 = 10\%$
For total male students: $\frac{40}{80}=0.5 = 50\%$
For total female students: $\frac{40}{80}=0.5 = 50\%$
For total Spanish students: $\frac{38}{80}=0.475 = 47.5\%$
For total French students: $\frac{28}{80}=0.35 = 35\%$
For total German students: $\frac{14}{80}=0.175 = 17.5\%$
The relative - frequency table is:

	Male	Female	Total
French	$20\%$	$15\%$	$35\%$
German	$7.5\%$	$10\%$	$17.5\%$
Total	$50\%$	$50\%$	$100\%$

Step2: Find joint relative frequency of female French - studying student

The joint relative frequency of a female student who is studying French is the value in the cell corresponding to female and French in the relative - frequency table, which is $15\%$.

Step3: Make observations

Observation 1: The percentage of students studying Spanish is the highest among the three languages, at $47.5\%$.
Observation 2: The percentage of male and female students is equal overall ($50\%$ each), but the distribution of languages varies between genders. For example, more female students study Spanish compared to male students.

Answer:

Relative - frequency table:

	Male	Female	Total
French	$20\%$	$15\%$	$35\%$
German	$7.5\%$	$10\%$	$17.5\%$
Total	$50\%$	$50\%$	$100\%$

Joint relative frequency of female French - studying student: $15\%$
Observations:

1. The percentage of students studying Spanish is the highest among the three languages, at $47.5\%$.
2. The percentage of male and female students is equal overall ($50\%$ each), but the distribution of languages varies between genders. For example, more female students study Spanish compared to male students.