Question

What is the mean of a grouped data with frequencies 4, 7, 6 and class internals 5-10, 10-15, 15-20?

• A. 10.25
• B. 13.55
• C. 15.6
• D. 12

Answer 1

Answer: (B)

13.55

Answer 2

To find the mean of a grouped data, we follow these steps:

1. Calculate the class mark ($x_i$) for each class interval.
   The class mark is the midpoint of the class interval, calculated as (Lower Limit + Upper Limit) / 2.

   • For the class 5-10: $x_1 = \frac{5 + 10}{2} = \frac{15}{2} = 7.5$
   • For the class 10-15: $x_2 = \frac{10 + 15}{2} = \frac{25}{2} = 12.5$
   • For the class 15-20: $x_3 = \frac{15 + 20}{2} = \frac{35}{2} = 17.5$

2. Multiply each class mark ($x_i$) by its corresponding frequency ($f_i$) to get $f_i x_i$.

   • For the class 5-10 (frequency $f_1 = 4$): $f_1 x_1 = 4 \times 7.5 = 30.0$
   • For the class 10-15 (frequency $f_2 = 7$): $f_2 x_2 = 7 \times 12.5 = 87.5$
   • For the class 15-20 (frequency $f_3 = 6$): $f_3 x_3 = 6 \times 17.5 = 105.0$

3. Sum all the $f_i x_i$ values ($\sum f_i x_i$).
   $\sum f_i x_i = 30.0 + 87.5 + 105.0 = 222.5$

4. Sum all the frequencies ($\sum f_i$).
   $\sum f_i = 4 + 7 + 6 = 17$

5. Calculate the mean ($\overline{x}$) using the formula:
   $\overline{x} = \frac{\sum f_i x_i}{\sum f_i}$
   $\overline{x} = \frac{222.5}{17}$
   $\overline{x} \approx 13.088$

Comparing this calculated value with the given options, the calculated mean 13.088 is closest to 13.55 among the given options.