In: Statistics and Probability
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
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.