Question

find the mean derivation about median for the following data 3,9,5,3,12,10,18,4,7,19,21​

Answer 1

Answer:

Step-by-step explanation:

Arranging data in ascending order,

3,3,4,5,7,9,10,12,18,19,21

⇒  Number of observation (n)=11 (odd)

Median=(  

2

11+1

​

)  

th

obs=6  

th

obs

∴  Median(M)=9

Now, we calculate mean deviation about median

M.D.(M)=  

11

∑∣x  

i

​

−M∣

​

 

              =  

11

∣3−9∣+∣3−9∣+∣4−9∣+∣5−9∣+∣7−9∣+∣9−9∣+∣10−9∣+∣12−9∣+∣18−9∣+∣19−9∣+∣21−9∣

​

 

=  

11

6+6+5+4+2+0+1+3+9+10+12

​

 

=  

11

58

​

 

k=11

Answer 2

Step-by-step explanation:

Solution :

Arranging data in ascending order,

3,3,4,5,7,9,10,12,18,19,21

Here :

Number of observations n = 11 (odd)

Since n is odd,

Median= (11 + 1/2) th observation

=> (12/2) th observation

=> 6 th observation

=> 9

Now,

We calculate mean deviation about median

M.D.(M) = ∑ ∣xî − M∣ / 11

=> ( ∣3 − 9∣ + ∣3 − 9∣ + ∣4 − 9∣ + ∣5 − 9∣ + ∣7- 9∣ + ∣9 − 9∣ + ∣10 − 9∣ + ∣12 − 9∣ + ∣18 − 9∣ + ∣19 − 9∣ + ∣21 − 9∣ / 11)

=> 6+6+5+4+2+0+1+3+9+10+12 / 11

=> 58/ 11

=> 5.27