Question

A survey regarding the heights (in cm) of 50 girls of a class was conducted and the following data was obtained:
$\begin{array}{ccccccc}\text{Height (in cm)}& 120-130& 130-140& 140-150& 150-160& 160-170& \text{Total}\\ \text{Number of girls}& 2& 8& 12& 20& 8& 50\end{array}$
Find the mean, median and mode of the above data.

Answer 1

Let the assumed mean A be 145.
Class interval h = 10.

Class	Frequency fi	Midvalue xi	ui=((xi−A)/h)	fiui	C.F
120-130	2	125	-2	-4	2
130-140	8	135	-1	-4	10
140-150	12	145 = A	0	0	22
150-160	20	155	1	20	42
160-170	8	165	2	16	50
	N=50			∑(fiui)=24

(i) Mean

$\overline{x}$ = A+h(∑fiui/N)

= 145+10 x (24/50)

=145+4.8 = 149.8

(ii) N = 50, N/2 = 25

Cumulative frequency just after 25 is 42

Median class is 150-160

I = 150, h = 10, N = 50, c = 22, f = 20

Therefore,
Median
Me=I+h((N/2−c)/f)
=150+10(25−22/20)

= 30 + 10 x 3/20
= 150 + 1.5 = 151.5

(iii) Mode = 3 x median - 2 x mean

= 3 x 151.5 - 2 x 149.8 = 454.5 - 299.6

= 154.9

Thus, mean = 149.8, median = 151.5, mode = 154.9