Question

Calculate the median from the following data:
$\begin{array}{ccccccccc}\text{Height}& 135-140& 140-145& 145-150& 150-155& 155-160& 160-165& 165-170& 170-175\\ \text{(in cm)}& & & & & & & & \\ \text{No. of}& 6& 10& 18& 22& 20& 15& 6& 3\\ \text{boys}& & & & & & & & \end{array}$

Answer 1

We prepare the cumulative frequency table, as shown:

Class	Frequency (f)	Cumulative frequency
135-140	6	6
140-145	10	16
145-150	18	34
150-155	22	56
155-160	20	76
160-165	15	91
165-170	6	97
170-175	3	100
	N=Σf=100

N= 100

⇒N/2=50

The cumulative frequency greater than 50 is 56 and the corresponding class is 150-155.

Thus the median class is 150-155.

Therefore, l= 150, h = 5, f = 22,
c.f. of preceding class = 34 and N/2=50

Median,
M=l+((N/2−cf)/f)×h

Median=150+(50–34/22)×5


Median=150+3.64

Median=153.64

Hence, median is 153.64.