Question

If class mid-points in a frequency distribution of a group of persons are: 125, 132, 139, 146, 153, 160, 167, 174, 181 pounds, find:
(a) size of the class intervals, and
(b) the class boundaries.

Answer 1

From the mid-values the class size is calculated using the following formula.
Class Size = Mid value of one class - Mid value of the preceding class
Class Size = 132 - 125 = 7
Now, the upper and lower limit for each of the class intervals is calculated as follows.
$$\begin{gathered} \mathrm{Lower}\mathrm{limit}=\mathrm{Mid}\mathrm{value}-\frac{\mathrm{Class}\mathrm{Size}}{2} \\ \mathrm{or},\mathrm{Lower}\mathrm{limit}=\mathrm{Mid}\mathrm{value}-\frac{7}{2} \\ \mathrm{Upper}\mathrm{limit}=\mathrm{Mid}\mathrm{value}+\frac{\mathrm{Class}\mathrm{Size}}{2} \\ \mathrm{or},\mathrm{Upper}\mathrm{limit}=\mathrm{Mid}\mathrm{value}+\frac{7}{2} \end{gathered}$$

Mid Value	Class Interval
125 132 139 146 153 160 167 174 181	121.5 − 128.5 128.5 − 135.5 135.5 − 142.5 142.5 − 149.5 149.5 − 156.5 156.5 − 163.5 163.5 − 170.5 170.5 − 177.5 177.5 − 184.5