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Question

The Heights of 29 children are given in the table below :

Heights(in ft.)No. of children2.5−353−3.563.5−474−4.594.5−52

What is the median height of the children?

A
3.25 ft
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B
3.607 ft
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C
3.75 ft
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D
4.275 ft
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Solution

The correct option is C: 3.75 ft

Lets form the cumulative frequency table to evaluate the median,

C.IFrequency~(f)Cumulative Frequency~(cf)2.535533.565+6=11 (cf)(L) 3.547 (F)5+6+11=1844.595+6+11+9=274.5525+6+11+9+2=29N=29

Here, total no. of children =N=29 (An odd number)

Median = ((29+1)2)th observation =15th th observation.

It will come after 11 in cumulative frequency.

So, the Median class is 3.54.. and

Lower boundary L=3.5

Corresponding frequency (F)=7

Corresponding preceding cumulative frequency (cf)=11

Size of the class interval (h)=43.5=0.5=510=12

Now, the Median =L+(N2cfF)×h

=3.5+(29211)7×12

=3.5+(2922)2×7×12

=3.5+72×7×12

=3.5+14

=3.5+0.25

=3.75

Therefore, median height of the children is 3.75 ft.


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