Question

Calculate the median from the following data:
$\begin{array}{ccccccccc}\text{Height}& 137.5& 142.5& 147.5& 152.5& 157.5& 162.5& 167.5& 172.5\\ \text{(in cm)}& & & & & & & & \\ \text{No. of}& 6& 10& 18& 22& 20& 15& 6& 3\\ \text{boys}& & & & & & & & \end{array}$

Answer 1

We prepare the cumulative frequency table, as shown:

Height	Frequency (f)	Cumulative frequency
137.5	6	6
142.5	10	16
147.5	18	34
152.5	22	56
157.5	20	76
162.5	15	91
167.5	6	97
172.5	3	100
	N=Σf=100

Here N= 100 (which is even )
⇒N/2=50
and also N/2+1 = 51

The median will lie between 50th
and the 51th observation but from the table we can see both the 50th and 51th observation corresponding to 152.5 in column of height

Thus the median height of the given data is 152.5 cm.