Question

Fill in the blanks with numbers to show how to calculate the relative frequencies.

First period
Second period
Total
Brown
20
15
35
Green
8
6
14
Blue
4
9
13
Total
32
30
62
a) To find the JOINT relative frequency of a first-period student having brown eyes, divide choose your answer...
to get about
choose your answer...
b) To find the JOINT relative frequency of a first-period student having blue eyes, divide choose your answer... v to get about choose your answer...
c) To find the MARGINAL relative frequency of having green eyes, divide choose your answer... .
choose your answer...
• to get about

Answer 1

To calculate the relative frequencies, we'll use the following formulas:

1. **Joint relative frequency**:
\[
\text{Joint Relative Frequency} = \frac{\text{Frequency of the category}}{\text{Total Frequency}}
\]
where the total frequency refers to the total number of observations.

2. **Marginal relative frequency**:
\[
\text{Marginal Relative Frequency} = \frac{\text{Marginal total of category}}{\text{Grand total}}
\]
where the marginal total is the total of that category across all groups.

### a) Joint Relative Frequency of a First-Period Student Having Brown Eyes

To find the joint relative frequency of a first-period student having brown eyes:

- Frequency of first-period students having brown eyes = 20
- Total number of students = 62

So, the calculation will be:
\[
\text{Joint Relative Frequency} = \frac{20}{62}
\]
Calculating it gives approximately:
\[
\frac{20}{62} \approx 0.3226 \text{ or about } 32.26\%
\]

**Answer**:
To find the JOINT relative frequency of a first-period student having brown eyes, divide **20** by **62** to get about **0.3226**.

### b) Joint Relative Frequency of a First-Period Student Having Blue Eyes

To find the joint relative frequency of a first-period student having blue eyes:

- Frequency of first-period students having blue eyes = 4
- Total number of students = 62

So, the calculation will be:
\[
\text{Joint Relative Frequency} = \frac{4}{62}
\]
Calculating it gives approximately:
\[
\frac{4}{62} \approx 0.0645 \text{ or about } 6.45\%
\]

**Answer**:
To find the JOINT relative frequency of a first-period student having blue eyes, divide **4** by **62** to get about **0.0645**.

### c) Marginal Relative Frequency of Having Green Eyes

To find the marginal relative frequency of having green eyes:

- Marginal total of green eyes = 14 (summing both periods)
- Grand total = 62

So, the calculation will be:
\[
\text{Marginal Relative Frequency} = \frac{14}{62}
\]
Calculating it gives approximately:
\[
\frac{14}{62} \approx 0.2258 \text{ or about } 22.58\%
\]

**Answer**:
To find the MARGINAL relative frequency of having green eyes, divide **14** by **62** to get about **0.2258**.