Question

The median of the distribution given below is 14.4. Find the values of x and y, if the total frequency is 20. Class interval : 0 - 6 6 - 12 12 - 18 18 - 24 24 - 30 Frequency : 4 x 5 y 1

Answer 1

Answer:

Solution :-

  Class Interval          Frequency          Cumulative Frequency

     0 - 6                           4                                  4

     6 - 12                         x                                4 + x

    12 - 18                        5                                9 + x

    18 - 24                        y                                9 + x + y

     24 - 30                       1                               10 + x + y

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                                      20                                                 

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10 + x + y = 20

x + y = 20 - 10

x + y = 10

Median = 14.4 

So, Median class is 12 - 18

Median = l + [(N/2 - cf)*i]/f

l = Lower limit of the Median Class = 12

Class Interval = i = 6

Cumulative Frequency (cf) of the class before the Median Class = 4 + x

N = 20

N/2 = 20/2 = 10

f = frequency of the Median Class = 5

⇒ Median = l + [(N/2 - cf)*i]/2

⇒ 14.4 = 12 + {10 - (4 + x)*6]/5

⇒ 14.4 - 12 = {(10 - 4 - x)*6}/5

⇒ 2.4 = {(6 - x)*6}/5

⇒ 2.4 = (36 - 6x)/5

⇒ 2.4*5 = 36 - 6x

⇒ 12 = 36 - 6x

⇒ - 6x = 12 - 36

 - 6x = - 24

⇒ 6x = 24

x = 24/6

x = 4

Since, x + y = 10

4 + y = 10

y = 10 - 4

y = 6

So, the value of x is 4 and the value of y is 6.

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