Question

Consider the frequency distribution of the heights of 60 students of a class

Height (in cm)	No. of Students	Cumulative Frequency
150-155	16	16
155-160	12	28
160-165	9	37
165-170	7	44
170-175	10	54
175-180	6	60

The sum of the lower limit of the modal class and the upper limit of the median class is
(a) 310
(b) 315
(c) 320
(d) 330

Answer 1

(b) 315
The class having the maximum frequency is the modal class.

$$\begin{gathered} \mathrm{So},\mathrm{}\mathrm{the}\mathrm{}\mathrm{modal}\mathrm{}\mathrm{class}\mathrm{}\mathrm{is}\mathrm{}150-155\mathrm{and}\mathrm{}\mathrm{its}\mathrm{}\mathrm{lower}\mathrm{}\mathrm{limit}\mathrm{}\mathrm{is}\mathrm{}150. \\ \mathrm{Also},\mathrm{}\mathrm{N}=60 \\ \Rightarrow \frac{\mathrm{N}}{2}=30\mathrm{} \\ \mathrm{The}\mathrm{}\mathrm{cumulative}\mathrm{}\mathrm{freequency}\mathrm{just}\mathrm{}\mathrm{more}\mathrm{}\mathrm{than}\mathrm{}30\mathrm{}\mathrm{is}\mathrm{}37\mathrm{and}\mathrm{}\mathrm{its}\mathrm{}\mathrm{class}\mathrm{}\mathrm{is}\mathrm{}160-165,\mathrm{whose}\mathrm{}\mathrm{upper}\mathrm{}\mathrm{limit}\mathrm{}\mathrm{is}\mathrm{}165. \\ \therefore \mathrm{Required}\mathrm{}\mathrm{sum}=\left(150+165\right)=315 \end{gathered}$$