Question

In: Statistics and Probability

Calculate the 5 number summary and the interquartile range of the following data: 37, 23, 3,...

Calculate the 5 number summary and the interquartile range of the following data:

37, 23, 3, 52, 35, 27, 28, 30, 41, 59, 20, 31, 48, 13, 937, 23, 3, 52, 35, 27, 28, 30, 41, 59, 20, 31, 48, 13, 9

Solutions

Expert Solution

Solution: Given that 37,23,3,52,35,27,28,30,41,59,20,31,48,13,937,23,3,52,35,27,28,30,41,59,20,31,48,13,9

Minimum: 3
Quartile Q1: 21.5
Median: 30
Quartile Q3: 44.5
Maximum: 937

interquartile range: 23

Explanation:

Quartile Q1: 21.5

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 9 13 13 20 20 23 23 27 27 28 28 30 30 31 31 35 35 37 41 41 48 48 52 52 59 59 937   

So, the bottom half is

3 3 9 13 13 20 20 23 23 27 27 28 28 30   

The median of these numbers is 21.5.

= > Median = 30

The median of the data set is 30.

Explanation

The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

3 3 9 13 13 20 20 23 23 27 27 28 28 30 30 31 31 35 35 37 41 41 48 48 52 52 59 59 937   

So, the median is 30 .

= > Quartile Q3: 44.5

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 9 13 13 20 20 23 23 27 27 28 28 30 30 31 31 35 35 37 41 41 48 48 52 52 59 59 937   

So, the upper half is

31 31 35 35 37 41 41 48 48 52 52 59 59 937   

The median of these numbers is 44.5.

= > Interquartile range = 23

Explanation

The interquartile range is the difference between the third and first quartiles.

The third quartile is 44.5.

The first quartile is 21.5.

The interquartile range = 44.5 - 21.5 = 23.


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