To calculate the mean from the frequency distribution table, we will follow these steps:

1. Determine the midpoints (class marks) for each class interval.

The midpoint for each class interval is calculated by averaging the lower and upper boundaries of the interval:

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

So, let's calculate:

• For $60-69$: $\frac{60 + 69}{2} = 64.5$
• For $70-79$: $\frac{70 + 79}{2} = 74.5$
• For $80-89$: $\frac{80 + 89}{2} = 84.5$
• For $90-99$: $\frac{90 + 99}{2} = 94.5$

2. Multiply the midpoints by their respective frequencies to get the products.

$\text{Product} = \text{Midpoint} \times \text{Frequency}$

• For $60-69$ (Midpoint = 64.5, Frequency = 20): $64.5 \times 20 = 1290$
• For $70-79$ (Midpoint = 74.5, Frequency = 18): $74.5 \times 18 = 1341$
• For $80-89$ (Midpoint = 84.5, Frequency = 5): $84.5 \times 5 = 422.5$
• For $90-99$ (Midpoint = 94.5, Frequency = 2): $94.5 \times 2 = 189$

3. Sum the products and the frequencies.

$\text{Sum of products} = 1290 + 1341 + 422.5 + 189 = 3242.5$ $\text{Sum of frequencies} = 20 + 18 + 5 + 2 = 45$

4. Calculate the mean.

$\text{Mean} = \frac{\text{Sum of products}}{\text{Sum of frequencies}} = \frac{3242.5}{45} \approx 72.06$

Thus, the mean of the data is approximately 72.06.

Would you like further details or have any questions?

Here are 5 related questions for further practice:

1. How would you find the median from a frequency distribution table?
2. What is the formula to calculate the mode from a grouped data table?
3. Can you calculate the range of this dataset from the table?
4. How does the mean change if we increase the frequency of the first class interval by 5?
5. What is the significance of using midpoints in calculating the mean for grouped data?

Tip: Always ensure that the sum of the frequencies adds up correctly before proceeding to calculations for grouped data.