Question

Calculate arithmetic mean of the following frequency distribution:

Class	less than 10	10−20	20−30	30−40	40−50	50−60	more than 60
Frequency	5	12	18	22	6	4	3

Answer 1

It must be noted that the given distribution is an open ended distribution, that is, the first and the last class interval are not explicitly defined. As mean is based on all the items in the series, so for such distributions mean cannot be calculated accurately. ​
However, going by the symmetry of the distribution we assume the first and the last class interval to be (0- 10) and (60 - 70), respectively

Class Interval	Mid-Values (m)	Frequency (f)	fm
0 − 10 10 − 20 20 − 30 30 − 40 40 − 50 50 − 60 60 − 70	5 15 25 35 45 55 65	5 12 18 22 6 4 3	25 180 450 770 270 220 195
		∑f = 70	∑fm = 2110

Using the direct method to find the mean, we get
$$\begin{gathered} \overline{X}=\frac{\Sigma fm}{\Sigma f} \\ =\frac{2110}{70}=30.14 \end{gathered}$$
Hence, the mean of the given distribution is 30.14