Question

If 35 is removed from the data: 30, 34, 35, 36, 37, 38, 39, 40, then the median increased by
(a)2
(b)1.5
(c)1
(d)0.5

Answer 1

SOLUTION :  

The correct option is (d) : 0.5  

★★ Median of the data depends on the number of observations (n) .

• i) If n is odd then median= value of [(n+1)/2]th observation

• ii) If n is even then median= ½value of [ (n/2)th + (n/2 +1) th] observations.

Given : Data is in ascending order : 30, 34, 35, 36, 37, 38 ,39 ,40

Here, n = 8 (even)

Median= ½value of [ (n/2)th + (n/2 +1) th] observations.

Median = ½value of [ (8/2)th + (8/2 +1) th] observations.

= ½value of [ 4th + (4 +1) th] observations.

= ½value of [ 4th + 5th] observations.

Median = ½ [ 36 + 37] = 73/2 = 36.5

Median = 36.5  

If 35 is removed than the new data is :

Data is in ascending order : 30, 34,36, 37, 38 ,39 ,40

Here, n = 7 (odd)

Median = value of [(n+1)/2]th observation

Median = value of [(7+1)/2]th observation

= value of [8/2]th observation

= value of 4th observation

Median = 37

The Median increased by = 37 - 36.5 = 0.5  

Hence, the Median increased by 0.5 .

HOPE THIS ANSWER WILL HELP YOU.,..

Answer 2

Answer:

Step-by-step explanation:

Median = ½value of [ (8/2)th + (8/2 +1) th] observations.

= ½value of [ 4th + (4 +1) th] observations.

= ½value of [ 4th + 5th] observations.

Median = ½ [ 36 + 37] = 73/2 = 36.5

Median = 36.5  

If 35 is removed than the new data is :

Data is in ascending order : 30, 34,36, 37, 38 ,39 ,40

Here, n = 7 (odd)

Median = value of [(n+1)/2]th observation

Median = value of [(7+1)/2]th observation

= value of [8/2]th observation

= value of 4th observation

Median = 37

The Median increased by = 37 - 36.5 = 0.5