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Q.

The given table represents the heights (in cm) of 50 students in a class. Find the median height of the class.

Height (in cm)No. Of students
1568
1544
15510
1516
1577
1523
15312

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a

155.5 cm

b

153.5 cm

c

154.5 cm

d

152.5 cm

answer is A.

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Detailed Solution

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From the dataset, let us first calculate the cumulative frequency of data and find the total number of terms.

Height (in cm)No. Of studentsCumulative frequency
15166
15239
1531221
154425
1551035
156843
157750

We observe that the number of terms n = 50 (even)

Applying the formula of the median for an even number of terms:

So, Median =

(n2)th term + (n2 + 1)th term2

(502)th term + (502 + 1)th term2

25th term + 26th term2

For the 26th term, we will take the value for the next greatest term after 25. i.e. 35th term.

Thus, we will take 155 for the value of the 26th term.

154 + 1552

3092

= 154.5

Therefore, the median is 154.5 cm.

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