The mean of the following table will be:
Class-interval 0-2 2-4 4-6 6-8 8-10 Frequency (f) 3 1 5 4 7
The mean of the following table will be:
| Class-interval | 0-2 | 2-4 | 4-6 | 6-8 | 8-10 |
|---|---|---|---|---|---|
| Frequency (f) | 3 | 1 | 5 | 4 | 7 |
Show Hint
- $4.2$
- $5.4$
- $6$
- $6.1$
The Correct Option is B
Solution and Explanation
Step 1: Find the Midpoints (x) of Each Class Interval
The formula to find the midpoint is:
\[ \text{Midpoint} = \frac{\text{Upper limit} + \text{Lower limit}}{2} \]
Midpoint Table:
| Class Interval | Frequency (f) | Midpoint (x) |
|---|---|---|
| 0-2 | 3 | 1 |
| 2-4 | 1 | 3 |
| 4-6 | 5 | 5 |
| 6-8 | 4 | 7 |
| 8-10 | 7 | 9 |
Step 2: Calculate \( f \times x \)
The table for \( f \times x \) is as follows:
| Class Interval | f | f × x |
|---|---|---|
| 0-2 | 3 | 3 |
| 2-4 | 1 | 3 |
| 4-6 | 5 | 25 |
| 6-8 | 4 | 28 |
| 8-10 | 7 | 63 |
| Total | Σf = 20 | Σf x = 122 |
Step 3: Use the Formula for Mean
The formula to calculate the mean is:
\[ \bar{x} = \frac{\Sigma f x}{\Sigma f} = \frac{122}{20} = 6.1 \]
Step 4: Conclusion
The mean of the given frequency distribution is 6.1.
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