Question

What are the minimum, first quartile, median, third quartile, and maximum of the following data set?: 37, 42, 44, 46, 47, 49, 51, 53, 54, 55, 57, 61, 63

Answer 1

Minimum term is `37`, first quartile is `45`, median is `51`, third quartile is `55` and maximum is `63`.

Explanation:

To find the minimum, first quartile, median, third quartile, and maximum of the given data set, first arrange it in increasing order.

As the data is already arranged (in `37, 42, 44, 46, 47, 49, 51, 53, 54, 55, 57, 61, 63`), it is obvious that

`37` is minimum and `63` is maximum. As number of terms are 13, median (the middle term is `(13+1)/2` ie `7^th` term i.e,. `51`.

First quartile is `(13+1)/4` i.e. `7/2` term and hence we take average of `3^(rd)` and `4^(th)` term which is `45`.

Third quartile is `(13*3+1)/4` i.e. `10^(th)` term, which is `55`.

Hence, minimum term is `37`, first quartile is `45`, median is `51`, third quartile is `55` and maximum is `63`.