Question

1
, 12
2. Median of a data, arranged in ascending order 7, 10, 15, x, y, 27,30 is 17 and
when one more observation 50 is added to the data, the median has become 18
Find x and y.
Median of a frequency distribution​

Answer 1

Answer:

CASE 1 (1st ARRANGEMENT)

7 , 10 , 15 , x , y , 27 , 30

Here,

Middle most value is x (Median)

And Median = 17

So,

x = 17

CASE 2 (2nd ARRANGEMENT)

7 , 10 , 15 , x , y , 27 , 30 , 50

Here,

Middle most value is x and y

Also,

Median = 18

Their average will be the median

x + y ÷ 2 = 18

17 + y = 36

y = 36 - 17 = 19

y = 19

HOPE IT HELPS YOU

Answer 2

Answer :-

Value of x is 17 and the value of y is 19.

Explanation :-

Data arranged in ascending order = 7, 10, 15, x, y, 27, 30

Number of observations (n) = 7

Here n is odd

Given

Median = 17

Median of the data when is odd = {(n + 1)/2} th observation

⇒ 17 = {(7 + 1)/2} th observation

⇒ 17 = (8/2) th observation

⇒ 17 = 4 th observation

⇒ 17 = x [∵ 4th observation in the given data is x]

⇒ x = 17

If one observation 50 added to the data median = 18

Data in asscending order when 50 added = 7, 10, 15, 17 , y, 27, 30, 50

Number of observations (n) = 8

Here n is even

Given

Median = 18

Median of the data when n is even = Average of (n/2)th observation and {(n/2) + 1} th observation

⇒ 18 = Average of (8/2) th observation and {(8/2) + 1}th observation

⇒ 18 = Average of 4 th observation and (4 + 1) th observation

⇒ 18 = Average of 4th and 5th observations

⇒ 18 = Avervage of 17 and y [∵ 4th observation is 17 and 5th observation is y]

⇒ 18 = (17 + y)/2

⇒ 18(2) = 17 + y

⇒ 36 = 17 + y

⇒ 36 - 17 = y

⇒ 19 = y

⇒ y = 19

Therefore the value of x is 17 and the value of y is 19.