To find the approximate mean from a grouped frequency table, we can use the formula:

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

where:

• $x$ is the midpoint of each class.
• $f$ is the frequency of each class.

Let's find the midpoints for each data range, multiply each by its frequency, and then calculate the mean.

Step 1: Find the Midpoints

1. $60 - 64$: Midpoint = $\frac{60 + 64}{2} = 62$
2. $65 - 69$: Midpoint = $\frac{65 + 69}{2} = 67$
3. $70 - 74$: Midpoint = $\frac{70 + 74}{2} = 72$
4. $75 - 79$: Midpoint = $\frac{75 + 79}{2} = 77$
5. $80 - 84$: Midpoint = $\frac{80 + 84}{2} = 82$
6. $85 - 89$: Midpoint = $\frac{85 + 89}{2} = 87$
7. $90 - 94$: Midpoint = $\frac{90 + 94}{2} = 92$
8. $95 - 99$: Midpoint = $\frac{95 + 99}{2} = 97$
9. $100 - 104$: Midpoint = $\frac{100 + 104}{2} = 102$

Step 2: Multiply Midpoints by Frequencies

We calculate the product of each midpoint and its corresponding frequency, and then sum them up.

Let's calculate.The approximate mean for the given data set is 81.3, rounded to one decimal place.

Would you like more details or have any questions about this calculation? Here are some related questions to expand on this topic:

1. How would you calculate the median for a grouped frequency distribution?
2. What is the difference between mean, median, and mode?
3. How can we determine the range of a data set?
4. What are the advantages of using a grouped frequency table?
5. How would outliers affect the mean in a dataset?

Tip: For grouped data, always use the midpoints of intervals to estimate measures like the mean or variance.