Question

A survey regarding the heights (in cm) of 50 girls of a class was conducted and the following data was obtained:

Height in cm	120 – 130	130 – 140	140 – 150	150 – 160	160 – 170
No. of girls	2	8	12	20	8

Find the mean, median and mode of the above data.

Answer 1

We have the following

Height in cm	Mid value `(x_i)`	Frequency `(f_i)`	Cumulative frequency	`(f_i  × x_i)`
120 – 130	125	2	2	250
130 – 140	135	8	10	1080
140 – 150	145	12	22	1740
150 – 160	155	20	42	3100
160 – 170	165	8	50	1320
		`Ʃ f_i` = 50		`Ʃ f_i × x_i` = 7490

Mean, x = `(sum ( f_i xx x_i))/(sum f_i)`

              =`7490/50`

              = 149.8
Now, N = 50

⇒`N/2 =25`

The cumulative frequency just greater than 25 is 42 and the corresponding class is 150 –
160.
Thus, the median class is 150 – 160.
∴ l = 150, h = 10, f = 20, c = cf of preceding class = 22 and `N/2 =25`

Now,

Median, `M_e = l + { h xx ((N/2-c)/f)}`

                    =  `150+ { 10xx ((25-22)/20) }`

                    =` (150+ 10 xx 3/20)`

                   = 151.5
Mode = 3(median) – 2(mean)
                 = 3 × 151.5 – 2 × 149.8
                 = 154.9