To calculate the mean (average) of the given data, follow these steps:

1. Find the midpoint of each class interval (e.g., 50-54, 55-59, etc.).
2. Multiply each midpoint by the frequency of that class interval.
3. Sum the products from step 2.
4. Divide the sum by the total frequency to find the mean.

Step 1: Calculate midpoints of each class interval

For each class interval, the midpoint is the average of the lower and upper bounds:

$\text{Midpoint} = \frac{\text{Lower bound} + \text{Upper bound}}{2}$

• $\frac{50 + 54}{2} = 52$
• $\frac{55 + 59}{2} = 57$
• $\frac{60 + 64}{2} = 62$
• $\frac{65 + 69}{2} = 67$
• $\frac{70 + 74}{2} = 72$
• $\frac{75 + 79}{2} = 77$
• $\frac{80 + 84}{2} = 82$
• $\frac{85 + 89}{2} = 87$
• $\frac{90 + 94}{2} = 92$

Step 2: Multiply midpoints by frequencies

Now multiply each midpoint by its corresponding frequency:

• $52 \times 1 = 52$
• $57 \times 1 = 57$
• $62 \times 3 = 186$
• $67 \times 6 = 402$
• $72 \times 6 = 432$
• $77 \times 8 = 616$
• $82 \times 15 = 1230$
• $87 \times 18 = 1566$
• $92 \times 10 = 920$

Step 3: Sum of the products

$52 + 57 + 186 + 402 + 432 + 616 + 1230 + 1566 + 920 = 5461$

Step 4: Total frequency

The total frequency is: [ 1 + 1 + 3 + 6 + 6 + 8 +