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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

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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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