Question

7. x,5 7 9 0 12 15

Answer 1

The given data is:

x i 5 7 9 10 12 15 f i 8 6 2 2 2 6

The cumulative frequencies are given by writing first term of discrete frequency in the first row of cumulative frequency, and then add the corresponding terms of cumulative frequency and discrete frequency. The table corresponding to the cumulative frequency is shown below:

x i	f i	c.f.
5	8	8
7	6	8+6=14
9	2	14+2=16
10	2	16+2=18
12	2	18+2=20
15	6	20+6=26
	∑ i=1 n f i =26

Since N = 26, median is calculated as the mean of ( n 2 ) th and ( n 2 +1 ) th

M= ( n 2 ) th + ( n 2 +1 ) th 2

M= ( 26 2 ) th + ( 26 2 +1 ) th 2 = 13 th + 14 th 2 = 7+7 2 =7

[Note: Both the 13th and 14th observations are = 7]

Therefore, the median of the given data is 7.

The formula to calculate the absolute deviation of the respective observations of the data is,

| x i −M |

Now make a table by using the above formula and using discrete frequency.

x i	f i	| x i −M |	f i | x i −M |
5	8	2	16
7	6	0	0
9	2	2	4
10	2	3	6
12	2	5	10
15	6	8	48
	∑ i=1 n f i =26		∑ i=1 n f i | x i −M | =84

M.D= ∑ i=1 n f i | x i −M | ∑ i=1 n f i M.D= 1 N ∑ i=1 n f i | x i −M | (2)

Substitute 26 for N and 84for ∑ i=1 n f i | x i −M | in equation (2).

M.D.= 84 26 =3.23

Therefore, the mean deviation of the given data is 3.23.