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# The Following is the Distribution of Height of Students of a Certain Class in a Certain City: - CBSE Class 10 - Mathematics

#### Question

The following is the distribution of height of students of a certain class in a certain city:

 Height (in cm): 160 - 162 163 - 165 166 - 168 169 - 171 172 - 174 No. of students: 15 118 142 127 18

Find the median height.

#### Solution

First we prepare the following cummulative table to compute the median.

 Height (in cm) Frequency (f1) Cumulative Frequency (c.f) 160 - 162 15 15 163 - 165 118 133 166 - 168 142 275 169 - 171 127 402 172 - 174 18 420 N = 420

Now, N = 420

thereforeN/2=420/2=210

Thus, the cumulative frequency just greater than 210 is 275 and the corresponding class is 166 - 168.

Therefore, 166 - 168 is the median class.

l = 166, f = 142, F = 133 and h = 2

We know that,

Median =l+{(N/2-F)/f}xxh

=166+{(210-133)/142}xx2

=166+(77xx2)/142

=166+154/142

= 166 + 1.08

= 167.08

Hence, the median height is approximately 167.1 cm.

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Solution The Following is the Distribution of Height of Students of a Certain Class in a Certain City: Concept: Median of Grouped Data.
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