Question

you randomly survey students in your school about the color of their eyes. the results are shown in the tables.
eye color of males surveyed
green: 5, blue: 16, brown: 27
eye color of females surveyed
green: 3, blue: 19, brown: 18
11
a. complete the two-way table
two - way table with columns: eye color (green, blue, brown, total) and rows: gender (male, female, total). filled values: male - green: 5, blue: 16, brown: 27, total: 48; female - green: 3, blue: 19, brown: 18, total: 40; total - green: 8, blue: 35, brown: 45, total: 88
b. interpret the...

Explanation:

Part a: Completing the Two - Way Table

Step 1: Calculate the total for Green eye color

To find the total number of students with green eyes, we add the number of males with green eyes and females with green eyes. The number of males with green eyes is 5 and the number of females with green eyes is 3. So, the total for green eyes is $5 + 3=8$.

Step 2: Calculate the total for Blue eye color

We add the number of males with blue eyes (16) and females with blue eyes (19). So, the total for blue eyes is $16+19 = 35$.

Step 3: Calculate the total for Brown eye color

We add the number of males with brown eyes (27) and females with brown eyes (18). So, the total for brown eyes is $27 + 18=45$.

Step 4: Calculate the total number of males

We add the number of males with green (5), blue (16), and brown (27) eyes. So, the total number of males is $5+16 + 27=48$.

Step 5: Calculate the total number of females

We add the number of females with green (3), blue (19), and brown (18) eyes. So, the total number of females is $3+19+18 = 40$.

Step 6: Calculate the grand total

We add the total number of males (48) and females (40). So, the grand total is $48+40 = 88$.

The completed two - way table is:

Gender\Eye Color	Green	Blue	Brown	Total
Female	3	19	18	40
Total	8	35	45	88

Part b: Interpreting the marginal frequencies

Marginal frequencies are the totals in the "Total" row and "Total" column.

• The marginal frequency for green eyes (total number of students with green eyes) is 8. This means that out of all the surveyed students, 8 have green eyes.
• The marginal frequency for blue eyes is 35. So, 35 out of the surveyed students have blue eyes.
• The marginal frequency for brown eyes is 45. So, 45 out of the surveyed students have brown eyes.
• The marginal frequency for males is 48. This means 48 males were surveyed.
• The marginal frequency for females is 40. This means 40 females were surveyed.
• The grand marginal frequency (total number of students surveyed) is 88. So, a total of 88 students were surveyed.

For example, if we want to know the proportion of students with brown eyes, we can use the marginal frequency of brown eyes (45) and the grand total (88). The proportion is $\frac{45}{88}\approx0.511$ or 51.1%, which means that about 51.1% of the surveyed students have brown eyes.

Answer:

Part a: Completing the Two - Way Table

Step 1: Calculate the total for Green eye color

To find the total number of students with green eyes, we add the number of males with green eyes and females with green eyes. The number of males with green eyes is 5 and the number of females with green eyes is 3. So, the total for green eyes is $5 + 3=8$.

Step 2: Calculate the total for Blue eye color

We add the number of males with blue eyes (16) and females with blue eyes (19). So, the total for blue eyes is $16+19 = 35$.

Step 3: Calculate the total for Brown eye color

We add the number of males with brown eyes (27) and females with brown eyes (18). So, the total for brown eyes is $27 + 18=45$.

Step 4: Calculate the total number of males

We add the number of males with green (5), blue (16), and brown (27) eyes. So, the total number of males is $5+16 + 27=48$.

Step 5: Calculate the total number of females

We add the number of females with green (3), blue (19), and brown (18) eyes. So, the total number of females is $3+19+18 = 40$.

Step 6: Calculate the grand total

We add the total number of males (48) and females (40). So, the grand total is $48+40 = 88$.

The completed two - way table is:

Gender\Eye Color	Green	Blue	Brown	Total
Female	3	19	18	40
Total	8	35	45	88

Part b: Interpreting the marginal frequencies

Marginal frequencies are the totals in the "Total" row and "Total" column.

• The marginal frequency for green eyes (total number of students with green eyes) is 8. This means that out of all the surveyed students, 8 have green eyes.
• The marginal frequency for blue eyes is 35. So, 35 out of the surveyed students have blue eyes.
• The marginal frequency for brown eyes is 45. So, 45 out of the surveyed students have brown eyes.
• The marginal frequency for males is 48. This means 48 males were surveyed.
• The marginal frequency for females is 40. This means 40 females were surveyed.
• The grand marginal frequency (total number of students surveyed) is 88. So, a total of 88 students were surveyed.

For example, if we want to know the proportion of students with brown eyes, we can use the marginal frequency of brown eyes (45) and the grand total (88). The proportion is $\frac{45}{88}\approx0.511$ or 51.1%, which means that about 51.1% of the surveyed students have brown eyes.