Question

In a grouped frequency distribution with class intervals 10-20, 20-30, and 30-40 with frequencies 5, 10, and 15 respectively, what is the mean if the total number of observations is 30?

Answer 1

28.33

Answer 2

To find the mean of a grouped frequency distribution, 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 10-20: $x_1 = \frac{10 + 20}{2} = \frac{30}{2} = 15$
   • For the class 20-30: $x_2 = \frac{20 + 30}{2} = \frac{50}{2} = 25$
   • For the class 30-40: $x_3 = \frac{30 + 40}{2} = \frac{70}{2} = 35$

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

   • For the class 10-20 (frequency $f_1 = 5$): $f_1 x_1 = 5 \times 15 = 75$
   • For the class 20-30 (frequency $f_2 = 10$): $f_2 x_2 = 10 \times 25 = 250$
   • For the class 30-40 (frequency $f_3 = 15$): $f_3 x_3 = 15 \times 35 = 525$

3. Sum all the $f_i x_i$ values ($\sum f_i x_i$).
   $\sum f_i x_i = 75 + 250 + 525 = 850$

4. Sum all the frequencies ($\sum f_i$).
   The total number of observations is given as 30, which is $\sum f_i$.
   Alternatively, we can sum the given frequencies: $\sum f_i = 5 + 10 + 15 = 30$.

5. Calculate the mean ($\overline{x}$) using the formula:
   $\overline{x} = \frac{\sum f_i x_i}{\sum f_i}$
   $\overline{x} = \frac{850}{30}$
   $\overline{x} = \frac{85}{3}$
   $\overline{x} \approx 28.33$

The mean of the given grouped frequency distribution is approximately 28.33.