Question

find the mean deviation about the median for the following data 6,7,10,12,13,4,8,12​

Answer 1

Answer

Solution

verified

Given data 6,7,10,12,13,4,12,16

first of all arrange data in ascending order

4,6,7,10,12,12,13,16

Here observe that no of observations is even i.e. n=8

So average of  

Median is  

2

n

​

th term and (  

2

n

​

+1)  

th

 term

Median =  

2

2

n

​

 

th

term+(  

2

n

​

+1)  

th

term

​

 

=  

2

2

8

​

 

th

term+(  

2

8

​

+1)  

th

term

​

 

=  

2

4  

th

term+5  

th

term

​

 

=  

2

10+12

​

=  

2

22

​

=11

(M) median =11

Now, we calculate mean deviation about median

we know that mean deviation about median =  

8

∑(x  

i

​

−M)

​

 

M.D(M)=  

8

∣4−11∣+∣6−11∣+∣7−11∣+∣10−11∣+∣12−11∣+∣12−11∣+∣13−11∣+∣16−11∣

​

 

                  =  

8

7+5+4+1+1+1+2+5

​

     we know ∣−x∣=x∣+x∣=x

                  =  

8

26

​

 

                  =3.25

mean deviation about median (M.D(M))=3.25