5 Number Summary Calculator / Interquartile Range Calculator

5 Number Summary / Interquartile Range Calculator

Data set (values separated by commas, maximum 50 values): * 211,169,280,232,210,257,170,228,100,290,247,168,148,158,252,261,189,233

Answer:

The 5 number summary of the data values:

Min: 1001st quartile: 169Median: 219.53rd quartile: 252Max: 290Interquartile range: 83

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

100, 148, 158, 168, 169, 170, 189, 210, 211, 228, 232, 233, 247, 252, 257, 261, 280, 290

Min and Max:

Once the data is sorted, it's easy to see that the minimum data value is 100 and the maximum data value is 290.

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 18 data values, the middle numbers are the data values at positions 9 and 10. These are 211 and 228. The median is the average of these numbers. We have $$ {\frac{ 211 + 228 }{2}} $$ Therefore, the median is $$ 219.5 $$

Q1, 25th percentile

To find the first quartile, or 25th percentile, list all the numbers in the data set from position 1 to position 9. These are the positions in the data set that are less than the position of the median.

100, 148, 158, 168, 169, 170, 189, 210, 211,

Now, we find the median of this smaller data set. That is the first quartile, Q1. Since there is an odd number of data values in this data set, there is only one middle number. With 9 data values, the middle number is the data value at position 5. Therefore, Q1, the 25th percentile, is 169.

Q3, 75th percentile

To find the third quartile, or 75th percentile, list all the numbers in the data set from position 10 to position 18. These are the positions in the data set that are more than the position of the median.

228, 232, 233, 247, 252, 257, 261, 280, 290,

Now, we find the median of this smaller data set. That is the third quartile, Q3. Since there is an odd number of data values in this data set, there is only one middle number. With 9 data values, the middle number is the data value at position 5. Therefore, Q3, the 75th percentile, is 252.

Interquartile range:

To find the interquartile range, subract Q1, 169, from Q3, 252. $$ 252 - 169 = 83 $$