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Q.

An incomplete distribution is given below:

You are given that the median value is 46 and the total number of items is 230.

Using the median formula and fill up missing frequencies.

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a

54,36

b

34,46

c

94,46

d

34,96

answer is B.

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Detailed Solution

Given is a table, median is 46 and total number of items is 230.
Question Image

Question Image

Median divides the data into upper half and lower half observations.
The frequency distribution table for data above for the data is as follows:
Question Image

Question Image

So,

x + y + 150 = 230 ⇒ x + y = 230 − 150 ⇒ x + y = 80............ 1

The expression for median is given as,

x ¯ = l + N 2 − c f f × h

, where N is the number of total observations, cf is cumulative frequency of class before median class, f is frequency of median class, h is class interval, l is lower interval.

⇒ 46 = 40 + 115 − x − 42 60 10 ⇒ 610 = 73 − x 65 ⇒ 39 = 73 − x ⇒ x = 73 − 39 ⇒ x = 34

Substituting

3

for

x

in the equation

1

,

⇒ x + y = 80 ⇒ y = 80 − 34 ⇒ y = 46

Thus, the values of x is 34 and y is 46.
Therefore, option (2) is correct.

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