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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.

Approximately find the mean for the following data set: Data: [60-64, 65-69, 70-74, 75-79, 80-84, 85-89, 90-94, 95-99, 100-104]; Frequency: [4, 8, 10, 5, 9, 7, 10, 14, 2]. Report answer accurate to one decimal place.

Learn how to calculate the mean for grouped data with a frequency distribution. This example walks through finding midpoints, multiplying by frequencies, and calculating the mean. Suitable for Grades 9-11 students.

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