Question

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

• A. $4.2$
• B. $5.4$
• C. $6$
• D. $6.1$

Hint:

To find the mean of a frequency table, multiply each class midpoint by its frequency, sum the results, and divide by the total frequency.

Answer 1

The Correct Option is B

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.