Find the mean for the data items in the given frequency distribution.

​Score, **x**

1

2

3

4

5

6

7

8

​Frequency, **f**

2

3

3

5

5

3

2

2

To find the mean of a frequency distribution, we use the formula:

\[
\text{Mean} = \frac{\sum (x \cdot f)}{\sum f}
\]

Where:
- \( x \) = score (data value)
- \( f \) = frequency (the number of times the score appears)

We first calculate \( x \cdot f \) for each score, then sum the products and divide by the total frequency.

| **Score (x)** | **Frequency (f)** | **\( x \cdot f \)** |
|---------------|-------------------|---------------------|
| 1             | 2                 | 1 × 2 = 2           |
| 2             | 3                 | 2 × 3 = 6           |
| 3             | 3                 | 3 × 3 = 9           |
| 4             | 5                 | 4 × 5 = 20          |
| 5             | 5                 | 5 × 5 = 25          |
| 6             | 3                 | 6 × 3 = 18          |
| 7             | 2                 | 7 × 2 = 14          |
| 8             | 2                 | 8 × 2 = 16          |

### Step 1: Sum of \( x \cdot f \)
\[
2 + 6 + 9 + 20 + 25 + 18 + 14 + 16 = 110
\]

### Step 2: Sum of the frequencies \( \sum f \)
\[
2 + 3 + 3 + 5 + 5 + 3 + 2 + 2 = 25
\]

### Step 3: Calculate the mean
\[
\text{Mean} = \frac{110}{25} = 4.4
\]

Thus, the mean score is **4.4**.

---

Would you like further details or explanations on any of the steps?

Here are five related questions:
1. How would you calculate the median for this frequency distribution?
2. How does changing a frequency value affect the mean?
3. What is the mode for the given frequency distribution?
4. How is the range of a data set calculated, and what is it for this set?
5. Can you explain how weighted averages differ from regular means?

**Tip:** Always check the total frequency to ensure you haven't missed any values when calculating the mean!

Find the mean for the data items in the given frequency distribution.

Learn how to calculate the mean of a frequency distribution using the given data set: Score (x) and Frequency (f). This example breaks down the steps, including calculating Σ(x * f) and Σf, to find the mean. Suitable for students in Grades 7-9.

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