Question

What is the mean of a grouped data with frequencies 4, 7, 8 and class internals 5-10, 10-15, 15-20?

Answer 1

13.55

Answer 2

To find the mean of grouped data, we use the formula: $\overline{x} = \frac{\sum f_i x_i}{\sum f_i}$ where $f_i$ are the frequencies and $x_i$ are the class marks (midpoints) of the class intervals.

1. Calculate the class mark ($x_i$) for each class interval:

   • 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 $f_3 = 8$): $f_3 x_3 = 8 \times 17.5 = 140.0$

3. Sum all the $f_i x_i$ values ($\sum f_i x_i$): $\sum f_i x_i = 30.0 + 87.5 + 140.0 = 257.5$

4. Sum all the frequencies ($\sum f_i$): $\sum f_i = 4 + 7 + 8 = 19$

5. Calculate the mean ($\overline{x}$): $\overline{x} = \frac{\sum f_i x_i}{\sum f_i} = \frac{257.5}{19} \approx 13.5526$

Rounding to two decimal places, the mean is 13.55.