Question

find the mean deviation from the median xi 15 9 7 11 17 5 13 fi 12 6 4 8 8 2 10
For me, the answer is not matching I am getting 3.12

Answer 1

Answer:

Step-by-step explanation:

The given

observations are already in ascending order.

Adding a column corresponding to cumulative

frequencies of the given data, we obtain the

x  

i

​

 f  

i

​

 c.f.

5 8 8

7 6 14

9 2 16

10 2 18

12 2 20

15 6 26

Here N=26

which is even

Median is

the mean of 13th and 14th observations. Both of these observations lie in the

cumulative frequency 14, for which the corresponding observation is 7

∴Median=  

2

13  

th  

 observation +14  

th  

 observation  

​

=  

2

7+7

​

=7

The absolute values of the deviations from median,

ie. ∣x  

i

​

−M∣, are

∣x  

i

​

−M∣  2 0 2 3 5 8

f  

i

​

  8 6 2 2  2 6

f  

i

​

∣x  

i

​

−M∣  16  0  4  6 10  48

 

i=1

∑

6

​

f  

i

​

=26 and  

i=1

∑

6

​

f  

i

​

∣x  

i

​

−M∣=84

M.D. (M)=  

N

1

​

 

i=1

∑

6

​

f  

i

​

∣x  

i

​

−M∣=  

26

1

​

×84=3.23