Calculate Mean , Median and Mode for the following data.
| Class interval | 10-14 | 15-19 | 20-24 | 25-29 | 30-34 | 35-39 | 40-45 |
| Frequency | 4 | 6 | 7 | 15 | 10 | 5 | 3 |
To calculate the Mean, Median, and Mode for the given data, we'll follow these steps:
### 1. Calculate the Mean
To find the mean of grouped data, we use the formula:
\[ \text{Mean} = \frac{\sum (f_i \cdot x_i)}{\sum f_i} \]
where \( f_i \) is the frequency of each class interval and \( x_i \) is the midpoint of each class interval.
Step-by-Step Calculation:
1. Determine the midpoints ( \( x_i \) ) of each class interval:
\[
\text{Midpoint of } 10-14 = \frac{10 + 14}{2} = 12
\]
\[
\text{Midpoint of } 15-19 = \frac{15 + 19}{2} = 17
\]
\[
\text{Midpoint of } 20-24 = \frac{20 + 24}{2} = 22
\]
\[
\text{Midpoint of } 25-29 = \frac{25 + 29}{2} = 27
\]
\[
\text{Midpoint of } 30-34 = \frac{30 + 34}{2} = 32
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