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.

Use the 5 number summary calculator to find the minimum, q1, median, q3, and maximum data values in a data set

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!

5 Number Summary / Interquartile Range Calculator

Answer:

The 5 number summary of the data values:

Min: 137
1st quartile: 151.5
Median: 199
3rd quartile: 267
Max: 278
Interquartile range: 115.5


Solution:

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 16 data values in this data set. It's helpful to sort them in ascending order.

$$ 137, 139, 143, 145, 158, 171, 179, 192, 206, 208, 251, 265, 269, 270, 273, 278 $$


Min and Max:

Once the data is sorted, it's easy to see that the minimum data value is 137 and the maximum data value is 278.


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 16 data values, the middle numbers are the data values at positions 8 and 9. These are 192 and 206. The median is the average of these numbers. We have $$ {\frac{ 192 + 206 }{2}} $$ Therefore, the median is $$ 199 $$


Q1, 25th percentile

To find the first quartile, or 25th percentile, list all the numbers in the data set from position 1 to position 8. These are the positions in the data set that are less than the position of the median.

$$ 137, 139, 143, 145, 158, 171, 179, 192, $$

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 8 data values, the middle numbers are the data values at positions 4 and 5. These are 145 and 158. The median is the average of these numbers. We have $$ {\frac{ 145 + 158 }{2}} $$ Therefore, Q1, the 25th percentile, is $$ 151.5 $$.


Q3, 75th percentile

To find the third quartile, or 75th percentile, list all the numbers in the data set from position 9 to position 16. These are the positions in the data set that are more than the position of the median.

$$ 206, 208, 251, 265, 269, 270, 273, 278, $$

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 8 data values, the middle numbers are the data values at positions 4 and 5. These are 265 and 269. The median is the average of these numbers. We have $$ {\frac{ 265 + 269 }{2}} $$ Therefore, Q3, the 75th percentile, is $$ 267 $$.


Interquartile range:

To find the interquartile range, subract Q1, 151.5, from Q3, 267. $$ 267 - 151.5 = 115.5 $$

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