Question

Find out the nedian size from the following:

X	160	150	152	161	156
f	5	8	6	3	7

Answer 1

X	f	Cumulative Frequency (cf)
150 152	8 6	8 14
156	7	21
160 161	5 3	26 29
	N=29

Median = size of ${\left(\frac{N+1}{2}\right)}^{\mathrm{th}}$ item
or, Median $=\frac{29+1}{2}={15}^{\mathrm{th}}\mathrm{item}$
Now, we need to locate this item in the column of Cumulative Frequency. The item exceeding 15^th is 21 (in the c.f. column), which is corresponding to 156. ​ Hence, median is 156.