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

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

Where:

• $x$ is the value of the variable,
• $f$ is the frequency of each $x$,
• $\sum{(x \cdot f)}$ is the sum of the products of $x$ and $f$,
• $\sum{f}$ is the sum of the frequencies.

Let’s break this down:

Step 1: Calculate the products $x \cdot f$

• For $x = 21$, $f = 4$, $x \cdot f = 21 \times 4 = 84$
• For $x = 22$, $f = 19$, $x \cdot f = 22 \times 19 = 418$
• For $x = 23$, $f = 10$, $x \cdot f = 23 \times 10 = 230$
• For $x = 24$, $f = 16$, $x \cdot f = 24 \times 16 = 384$
• For $x = 25$, $f = 17$, $x \cdot f = 25 \times 17 = 425$

Step 2: Sum the products $x \cdot f$

$\sum{(x \cdot f)} = 84 + 418 + 230 + 384 + 425 = 1541$

Step 3: Sum the frequencies $f$

$\sum{f} = 4 + 19 + 10 + 16 + 17 = 66$

Step 4: Calculate the mean

$\text{Mean} = \frac{1541}{66} = 23.35$

Rounding to 1 decimal place: $\text{Mean} = 23.4$

Would you like more details or have any other questions?

Here are 5 related questions to consider:

1. What does the mean represent in this context?
2. How would the mean change if the frequency for $x = 24$ increased by 10?
3. What is the difference between mean, median, and mode in this type of data?
4. How can you calculate the median of this frequency distribution? 5