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The distribution below gives the weights of 30 students of a class.

The median weight of the students is 56.67 kg.

Is the above statement true?

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True

False

answer is A.

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Detailed Solution

It is given a data,
Question Image

The given data is written as-
Question Image

The median class is the class having cumulative frequency (

c f

) just greater than

N 2

.
From the given data, number of observations N = 30
So,

N 2 = 302 = 15

Now, the class having cumulative frequency close to or greater than 15 is 55-60
Therefore, median class = 55-60
Now, for this median class
Lower limit l = 55
Class size h = 5
Frequency f = 6

c f

of the class preceding the median class = 13
Using the formula for median-

M e d i a n = l + n 2 − c f f × h

Substituting the values, we get

⇒ M e d i a n = 55 + 15 − 13 6 × 5

⇒ M e d i a n = 55 + 26 × 5

⇒ M e d i a n = 55 + 1.67

⇒ M e d i a n = M e d i a n = 56.67 k g

Hence, 56.67 kg is the required median weight.
Therefore, the given statement is true.
Hence option (1) is correct.

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