Class	Frequency
0-9	284
10-19	202
20-29	218
30-39	257
40-49	174
50-59	94
60-69	18
70-79	25
80-89	15
90-99	1

The mean is approximately

To calculate the approximate mean of the given data, we'll use the formula for the mean of a grouped frequency distribution:

\[
\text{Mean} = \frac{\sum (f \times x)}{\sum f}
\]

where:
- \( f \) is the frequency of each class,
- \( x \) is the midpoint of each class,
- \( \sum (f \times x) \) is the sum of the products of the midpoints and their respective frequencies,
- \( \sum f \) is the sum of all frequencies.

### Step 1: Calculate the midpoints for each class.
\[
\text{Midpoint} = \frac{\text{Lower limit} + \text{Upper limit}}{2}
\]

\[
\begin{array}{|c|c|c|}
\hline
\text{Class} & \text{Midpoint} (x) & \text{Frequency} (f) \\
\hline
0-9 & 4.5 & 284 \\
10-19 & 14.5 & 202 \\
20-29 & 24.5 & 218 \\
30-39 & 34.5 & 257 \\
40-49 & 44.5 & 174 \\
50-59 & 54.5 & 94 \\
60-69 & 64.5 & 18 \\
70-79 & 74.5 & 25 \\
80-89 & 84.5 & 15 \\
90-99 & 94.5 & 1 \\
\hline
\end{array}
\]

### Step 2: Multiply the midpoint by the frequency for each class.
\[
\sum (f \times x) = (4.5 \times 284) + (14.5 \times 202) + (24.5 \times 218) + \dots + (94.5 \times 1)
\]

\[
= 1278 + 2929 + 5341 + 8876.5 + 7743 + 5123 + 1161 + 1862.5 + 1267.5 + 94.5 = 33675
\]

### Step 3: Calculate the total frequency.
\[
\sum f = 284 + 202 + 218 + 257 + 174 + 94 + 18 + 25 + 15 + 1 = 1288
\]

### Step 4: Calculate the mean.
\[
\text{Mean} = \frac{33675}{1288} \approx 26.14
\]

So, the approximate mean of the data is **26.14**.

Would you like more details, or do you have any questions? 

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**Related Questions:**
1. How is the median calculated for a grouped frequency distribution?
2. What is the mode of this data set?
3. How does the mean change if the frequency of the 0-9 class is reduced?
4. What does the standard deviation tell us about this data set?
5. How can the mean be used to analyze the overall trend of the data?

**Tip:** Always verify the total frequency sum to ensure accuracy in calculating the mean for grouped data.

Learn how to calculate the mean of a grouped frequency distribution using the midpoint formula and weighted averages. This problem involves analyzing class frequency data across different age groups. Suitable for high school students studying statistics.

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