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.

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!