Question

6.10 30 50 70 90x,f 4·24 28 16 8

Answer 1

The given data is:

x i	10	30	50	70	90
f i	4	24	28	16	8

Now create a table as follows:

x i	f i	f i x i	| x i − x ¯ |	f i | x i − x ¯ |
10	4	40	40	160
30	24	720	20	480
50	28	1400	0	0
70	16	1120	20	320
90	8	720	40	320
	∑ i=1 n f i =80	∑ i=1 n x i f i =4000		∑ i=1 n f i | x i − x ¯ | =1280

The formula to calculate the mean when discrete frequency is given is,

x ¯ = ∑ i=1 n x i f i ∑ i=1 n f i x ¯ = 1 N ∑ i=1 n x i f i

Substitute 80 for N and 4000 for ∑ i=1 n x i f i in equation (1).

x ¯ = 4000 80 =50

Therefore, the mean of the given data is 50.

The formula to calculate the mean deviation about the mean is,

M.D= ∑ i=1 n f i | x i − x ¯ | ∑ i=1 n f i M.D= 1 N ∑ i=1 n f i | x i − x ¯ |

M.D.= 1280 80 =16

Therefore, the mean deviation of the given data is 16.