The 5 number summary calculator will show you a step by step way to find the min, Q1, median, Q3, and max values in a set. After finding Q1 and Q3, it will also find the interquartile range.
After finding the 5 number summary, another helpful resource is the Percentile Formula Calculator and the Percentile Rank Calculator. We make Statistics easy… You GOT this!
The 5 number summary of the data values:
Min: 114
1st quartile: 170.5
Median: 236.5
3rd quartile: 279.5
Max: 288
Interquartile range: 109
To find the 5 number summary of a data set, you need to find the smallest data value (minimum), the 25th percentile (Q1 - the first quartile), the median (25th percentile, Q2, the second quartile), the 75th percentile (Q3 - the third quartile), and the largest data value (maximum).
Take note that there are 20 data values in this data set. It's helpful to sort them in ascending order.
114, 117, 150, 162, 165, 176, 177, 217, 231, 233, 240, 252, 272, 275, 279, 280, 282, 284, 285, 288
Min and Max:
Once the data is sorted, it's easy to see that the minimum data value is 114 and the maximum data value is 288.
Median:
The median of a data set is found by identifying the middle number in a sorted data set. If there are an odd number of data values in the data set, the median is a single number. If there are an even number of data values in the data set, the median is the average of the two middle numbers.
Since there is an even number of data values in this data set, there are two middle numbers. With 20 data values, the middle numbers are the data values at positions 10 and 11. These are 233 and 240. The median is the average of these numbers. We have $$ {\frac{ 233 + 240 }{2}} $$ Therefore, the median is $$ 236.5 $$
Q1, 25th percentile
To find the first quartile, or 25th percentile, list all the numbers in the data set from position 1 to position 10. These are the positions in the data set that are less than the position of the median.
114, 117, 150, 162, 165, 176, 177, 217, 231, 233,
Now, we find the median of this smaller data set. That is the first quartile, Q1. Since there is an even number of data values in this data set, there are two middle numbers. With 10 data values, the middle numbers are the data values at positions 5 and 6. These are 165 and 176. The median is the average of these numbers. We have $$ {\frac{ 165 + 176 }{2}} $$ Therefore, Q1, the 25th percentile, is $$ 170.5 $$.
Q3, 75th percentile
To find the third quartile, or 75th percentile, list all the numbers in the data set from position 11 to position 20. These are the positions in the data set that are more than the position of the median.
240, 252, 272, 275, 279, 280, 282, 284, 285, 288,
Now, we find the median of this smaller data set. That is the third quartile, Q3. Since there is an even number of data values in this data set, there are two middle numbers. With 10 data values, the middle numbers are the data values at positions 5 and 6. These are 279 and 280. The median is the average of these numbers. We have $$ {\frac{ 279 + 280 }{2}} $$ Therefore, Q3, the 75th percentile, is $$ 279.5 $$.
Interquartile range:
To find the interquartile range, subract Q1, 170.5, from Q3, 279.5. $$ 279.5 - 170.5 = 109 $$