Question

Find the mean, median and mode of the following data: 

Classes:	0 – 50	50 – 100	100 – 150	150 – 200	200 – 250	250 – 300	300 – 350
Frequency:	2	3	5	6	5	3	1

Answer 1

Class interval	Mid value()x	Frequency(fi)	fixi	Cumulative frequency
0 – 50	25	2	50	2
50 – 100	75	3	225	5
100 – 150	125	5	625	10
150 – 200	175	6	1050	16
200 – 250	225	5	1125	21
250 – 300	275	3	825	24
300 – 350	325	1	325	25
		N = 25	`sumfx=4225`

Here, the maximum frequency is 6 so the modal class 150 − 200.

Therefore,

l = 150

h = 50

f = 6

f1 = 5

f2 = 5

F = 10

Mean `=(sumfx)/N=4225/25=169`

Thus, the mean of the data is 169.

We have N = 25 then N/2 = 12.5

Median `=l+(N/2-F)/fxxh`

`=150+(12.5-10)/6xx50`

`=150+2.5/6xx50`

`=150+125/6`

= 150 + 20.83

= 170.83

Thus, the median of the data is 170.83.

Mode `=l+(f-f1)/(2f-f1-f2)xxh`

`=150+(6-5)/(2xx6-5-5)xx50`

`=150+1/(12-10)xx50`

`=150+1/2xx50`

`=150+50/2`

= 150 + 25

= 175

Thus, the mode of the data is 175.