Question

The following data is from a random sample: 1, 1, 1, 2, 3, 5, 5, 8, 12, 13, 14, 14, 75, 75, 18, 100. What sets of numbers can be correct for the first, second and third quartiles?​

Answer 1

Answer:

2.5, 10, 44.5

Step-by-step explanation:

The median of second quartile divides the data into a lower half and an upper half.

The first quartile is the middle value of the lower half.

The third quartile is the middle value of the upper half.

For when there are $4n$ data :)

First Quartile : mean of the $n^{th}+(n+1)^{th}$ data

Second Quartile : mean of the $2n^{th}+(2n+1)^{th}$ data

Third quartile : mean of the $3n^{th}+(3n+1)^{th}$ data

Your Question : How to find the value of the quartiles?

First, arrange the data in ascending order.

$1, 1, 1, 2, 3, 5, 5, 8, 12, 13, 14, 14, 75, 75, 18, 100$

There are 16 data.

Hence, $4n=16$, $n=4$.

The lower quartile is mean of $4^{th}+5^{th}$ data.

The second quartile is mean of $8^{th}+9^{th}$ data.

The upper quartile is mean of $12^{th}+13^{th}$ data.

First, second and third quartile is 2.5, 10, 44.5.