Question

the median of the following data is 20.75. find the missing frequencies x and y,if the total frequency is 100.

Answer 1

Please refer the attachment..

Thank u..

Answer 2

The correct answer is x = 17 and y = 20.

Given: Number of frequency = 100.

Median = 20.75.

To Find: The missing frequencies x and y.

Solution:

Refer to the attachment for table of median.

63 + x + y = 100

x + y =37

y = 37 - x  (equation 1)

For median = 20.75 the median class = 20-25.

Lower limit (l) = 20

Frequency (f) = y

Frequency of preceding class = 30 + x

Class size (h) = 5

Put the values in the median formula.

Median = $l+(\frac{\frac{n}{2}-f }{f}) *h$

20.75 = $20+(\frac{\frac{100}{2}-(30+x) }{y\\}) *5$

20.75 =  $20+(\frac{50-30-x }{y\\}) *5$

0.75 = $(\frac{20-x}{y}) *5$

$\frac{3}{4} = \frac{100-5x}{y}$

3y = 400 - 20x

From equation 1,

3 (37 - x) = 400 - 20x

111 - 3x = 400 - 20x

-3x + 20x = 400-111

x = 17

Put value of x in equation 1.

y = 37 - x

y = 37 - 17

y = 20

Hence, the value of x = 17 and y = 20.

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