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Question

The given table shows the frequency according to the class intervals.

Class IntervalFrequency010101020520308304012405016

Find the Median value using Step jump method.


A

30

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B

37.6

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C

32.9

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D

27.67

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Solution

The correct option is C

32.9


The Cumulative frequency table for the given data can be drawn as :

Less thanCumulative Frequency10102015302340355051

N = 51 (An odd number)

Median = (51+1)2th observation = 26th observation.

So, the Median class is 30 - 40

We know that there are 12 observations from the 23rd observation to the 35th observation which come between 30 and 40.

However, we do not know their individual heights.

We will divide 10 from 30 to 40 into 12 equal parts and assume that one observation is in each subdivision.

We will assume that the value of each observation in a subdivision is the mid - value of the subdivision.

So, the the height of the 24th observation is the mid value of 30 and 301012ft, that is 301024

So, from the 24th observation to the 30th observation, there are 6 observations.

If the 24th term of the AP is 301024 and the common difference is 1012,

Then the 26th term = 301024 + 6×1012

= 30+10+12024

= 30 + 5.417

= 35.417


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