Question

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

Classes:	0-20	20-40	40-60	40-60	80-100	100-120	120-140
Frequency:	6	8	10	12	6	5	3

 

Answer 1

Consider the following data.

Class	Frequency (fi)	xi	fi xi	C.f.
0−20	6	10	60	6
20−40	8	30	240	14
40−60	10	50	500	24
60−80	12	70	840	36
80−100	6	90	540	42
100−120	5	110	550	47
120−140	3	130	390	50
	`N=sumf=50`		`sumf_1x_1=3120`

Here, the maximum frequency is 12 so the modal class is 60−80.

Therefore,

l = 60

h = 20

f = 12

f1 = 10

f2 = 6

F = 24

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

`=60+(25-24)/12xx20`

`=60+1/12xx20`

`=60+20/12`

= 60 + 1.67

= 61.67

Thus, the median of the data is 61.66.

 

Mean `=(sumf_1x_1)/sumf`

`=3120/50=32.4`

Thus, the mean of the data is 62.4.

 

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

`=60+(12-10)/(24-10-6)xx20`

`=60+2/8xx20`

`=60+40/8`

= 60 + 5

= 65

Thus, the mode of the data is 65.