Question

For the data set 3 4 6 5 10 5 12 3 28 5 7 5 10 6 5 23 14 3 6 5 7 12 Send data to Excel Part: 0 / 4 Part 1 of 4 (a) Find the first and third quartiles. The first quartile is The third quartile is

Answer 1

Solution: Given data set : 3,6,5,12,3,7,5,14,3,7,5,23,4,10,5,28,5,10,6,6,5,12

(a)
The first quartile is 5

The third quartile is 10
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Explanation

The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.

3 3 3 4 5 5 5 5 5 5 6 6 6 7 7 10 10 12 12 14 23 28   

So, the bottom half is

3 3 3 4 5 5 5 5 5 5 6   

The median of these numbers is 5.

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Explanation

The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.

3 3 3 4 5 5 5 5 5 5 6 6 6 7 7 10 10 12 12 14 23 28   

So, the upper half is

6 6 7 7 10 10 12 12 14 23 28   

The median of these numbers is 10.