Question

55. x510 15 20 25133

Answer 1

The given data is:

x i	5	10	15	20	25
f i	7	4	6	3	5

Now create a table as follows:

x i	f i	f i x i	| x i − x ¯ |	f i | x i − x ¯ |
5	7	35	9	63
10	4	40	4	16
15	6	90	1	6
20	3	60	6	18
25	5	125	11	55
	∑ i=1 n f i =25	∑ i=1 n x i f i =350		∑ i=1 n f i | x i − x ¯ | =158

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

x ¯ = 350 25 =14

Therefore, the mean of the given data is 14.

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.= 158 25 =6.32

Therefore, the mean deviation of the given data is 6.32.