Compute the median for each of the following data

Asked by admin @ 20/08/2021 in Math viewed by 346 People

(i) (ii)
Marks No of students Marks No of students
Less than 10 0 More than 80 150
Less than 30 10 More than 90 141
Less than 50 25 More than 100 124
Less than 70 43 More than 110 105
Less than 90 65 More than 120 60
Less than 110 87 More than 130 27
Less than 130 96 More than 140 12
Less than 150 100 More than 150 0

Answered by admin @ 20/08/2021

SOLUTION :

CUMULATIVE FREQUENCY TABLES are in the attachment.

(i)

Here, n = 100

n/2 = 50

Since, the Cumulative frequency just greater than 50 is 65 and the corresponding class is 70 - 90. Therefore 70 - 90 is the median class.

Here, l = 70 , f = 22 , c.f = 43, h = 20

MEDIAN = l + [(n/2 - cf )/f ] ×h

= 70 + [50 - 43)/22] × 20

= 70 + (7 × 20)/22

= 70 + (7 × 10)/11

= 70 + 70/11

= 70 + 6.36

= 76.36

Hence, the Median is 76.36.

(ii)

Here, n = 150

n/2 = 75

Since, the Cumulative frequency just greater than 75 is 105 and the corresponding class is 110 - 120. Therefore 110 - 120 is the median class.

Here, l = 120 , f = 45 , c.f = 60, h = -10 (class interval is in descending order)

MEDIAN = l + [(n/2 - cf )/f ] ×h

= 120 + [75 - 60)/45] × -10

= 120 + (15 × -10)/45

= 120 - 150/45

= 120 - 10/3

= 120 - 3.333

= 111.67 (approximate)

Hence, the Median is 111.67 (approximate)

★★ MEDIAN = l + [(n/2 - cf )/f ] ×h

Where,

l = lower limit of the median class

n = number of observations

cf = cumulative frequency of class interval preceding the median class

f = frequency of median class

h = class size

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