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To construct the frequency and relative frequency distributions for the scores provided, we need to:

1. Tally the frequencies of scores within each specified class interval.
2. Calculate the relative frequency for each class interval by dividing each class frequency by the total number of scores (48) and expressing it as a percentage.

Let’s go through each step:

### Step 1: Calculate the Frequencies

The class intervals are:
- **21-25**
- **26-30**
- **31-35**
- **36-40**
- **41-45**
- **46-50**

Counting the scores within each interval:

1. **21-25**: Count the scores in this range.
2. **26-30**: Count the scores in this range.
3. **31-35**: Count the scores in this range.
4. **36-40**: Count the scores in this range.
5. **41-45**: Count the scores in this range.
6. **46-50**: Count the scores in this range.

I’ll process these counts for each class.

### Step 2: Calculate Relative Frequencies

For each class:
\[
\text{Relative Frequency} = \left(\frac{\text{Class Frequency}}{\text{Total Frequency}}\right) \times 100
\]

The total frequency is 48. Let me proceed with the calculations.Here are the frequency and relative frequency distributions for the scores:

| Class Limits | Frequency (f) | Relative Frequency (%) |
|--------------|---------------|------------------------|
| 21-25        | 1             | 2.1%                  |
| 26-30        | 2             | 4.2%                  |
| 31-35        | 4             | 8.3%                  |
| 36-40        | 8             | 16.7%                 |
| 41-45        | 19            | 39.6%                 |
| 46-50        | 14            | 29.2%                 |

Would you like further details or have any questions?

### Related Questions:
1. How would we interpret the highest relative frequency in this data set?
2. How can we visualize this data with a histogram?
3. What insights can we draw from the distribution of scores?
4. How do we calculate cumulative frequency from this data?
5. What would happen to the relative frequencies if we had a larger sample size?

#### Tip:
The sum of relative frequencies should always approximate 100%, as it represents the entire data set in percentage terms.

Construct frequency and relative frequency distributions for the scores of a sociology class on a 50-point exam.

Calculate the frequency and relative frequency distribution for sociology class exam scores. This problem covers statistical concepts like frequency and relative frequency calculation. Suitable for high school students in Grades 10-12.

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