Five Number Summary Calculator with Step-by-Step Solution

Five Number Summary Calculator Sign

This calculator will find an entered data set's minimum value, first quartile, median, third quartile, maximum value, and interquartile range.

Plus, the calculator generates the step-by-step solution and a visual representation of the results.

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Five Number Summary Calculator

Calculate the five-number summary of a data set, and see the step-by-step solution.
Special Instructions

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Selected Data Record:

A Data Record is a set of calculator entries that are stored in your web browser's Local Storage. If a Data Record is currently selected in the "Data" tab, this line will list the name you gave to that data record. If no data record is selected, or you have no entries stored for this calculator, the line will display "None".

DataData recordData recordSelected data record: None

Load or Clear Sample Data Set:

To quickly see how the 5-Number Summary Calculator works, tap the "Sample" button. To clear sample entries, tap the "Clear" button.

Enter or paste data set:Enter or paste data set:Enter or paste data set:Enter or paste data set:

Data set:

Enter each element of the data set (or paste a copied data set) into this text box. Be sure each number is separated by a space, a comma, a line return, or any combination of the three.

Elements:# of elements:Number of elements in set:Numbers of elements in set:

Number of elements in set:

This is the total number of elements detected in the data set field.

Minimum:Minimum:Minimum:Minimum:

Minimum:

This is the minimum or smallest value in the data set.

Q1:1st quartile:1st quartile (lower):First quartile (Q1/lower):

1st quartile (lower):

This is the 1st quartile of the data set based on the interpolation method, which is just one of many methods that can be used. The larger the data set, the closer the results of all methods will be to each other.

Median:Median:Median (middle value):Median (middle value):

Median:

This is the median of the data set based on the interpolation method of calculating quartiles, which is just one of many methods that can be used. The larger the data set, the closer the results of all methods will be to each other.

Q3:3rd quartile:Third quartile (upper):Third quartile (Q3/upper):

Third quartile (upper):

This is the third quartile of the data set based on the interpolation method of calculating quartiles, which is just one of many methods that can be used. The larger the data set, the closer the results of all methods will be to each other.

Maximum:Maximum:Maximum:Maximum:

Maximum:

This is the maximum or largest value in the data set.

Inter range:Interquartile range:Interquartile range:Interquartile range:

Interquartile range:

This is the interquartile range, which results from of subtracting Q1 from Q3.

If you would like to save the current entries to the secure online database, tap or click on the Data tab, select "New Data Record", give the data record a name, then tap or click the Save button. To save changes to previously saved entries, simply tap the Save button. Please select and "Clear" any data records you no longer need.

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Help and Tools

Learn

What a 5-Number Summary is and How to Calculate it.

What is a five-number summary?

The 5-number summary gives you a quick snapshot of the distribution of a data set using five descriptive statistics.

The five descriptive statistics are:

  • Minimum (smallest)
  • 1st quartile (lower quartile)
  • Median (middle value)
  • 3rd quartile (upper quartile)
  • Maximum (largest)

The summary can then be used to compare data sets, especially when converted into visual representations called box plots or box and whisker plots.

How to Calculate Five Number Summary

To illustrate how to calculate a 5-number summary, let's use the following example data set:

90, 130, 400, 200, 350, 70, 325, 250, 150, 275, 270, 150, 130, 59, 200, 450, 300, 220, 100, 200, 400, 200, 250, 95, 180, 170, 150

I used the following steps to calculate the Five Number Summary. Please note that the method I use for calculating quartiles is only one of many different methods that can be used.

Sort Data Set In Descending Order

PositionValue
159
270
390
495
5100
6130
7130
8150
9150
10150
11170
12180
13200
14200
15200
16200
17220
18250
19250
20270
21275
22300
23325
24350
25400
26400
27450

Find the Minimum and Maximum

Based on the table above, the minimum value in the data set is 59, and the maximum value in the data set is 450.

Find the 1st Quartile (Lower)

To find the position of the 1st quartile (lower), we solve for the following equation, where n is equal to the number of values in the set (27):

Q1 Position= 0.25(n + 1)
 = 0.25(27+ 1)
 = 0.25 x 28
 = 7

Since 7 is an integer, the 1st quartile is the value in the 7th position, which is 130.

Find the Median (Middle)

To find the position of the middle value we solve for the following equation, where n is equal to the number of values in the set (27):

Median Position= 0.50(n + 1)
 = 0.50(27+ 1)
 = 0.50 x 28
 = 14

Since 14 is an integer, the median is the value in the 14th position, which is 200.

Find the 3rd Quartile (Upper)

To find the position of the 3rd quartile, we solve for the following equation, where n is equal to the number of values in the set (27):

Q3 Position= 0.75(n + 1)
 = 0.75(27+ 1)
 = 0.75 x 28
 = 21

Since 21 is an integer, the 3rd quartile is the value in the 21st position, which is 275.

Below are the color-coded results of my 5 Number Summary calculations for the entered set of data, followed by my attempt to create a rough visual presentation of the summary (hopefully somewhat similar to an official Box and Wisper Plot).

5 Number Summary
Minimum59
Q1 (Lower)130
Median (Middle)200
Q3 (Upper)275
Maximum450
500 -
410 -
320 -
230 -
140 -

But what about a data set that does not yield integers for positions? In that case, we can use interpolation to find the median and quartiles. To show how interpolating is used, let's remove the last value from the earlier example:

90, 130, 400, 200, 350, 70, 325, 250, 150, 275, 270, 150, 130, 59, 200, 450, 300, 220, 100, 200, 400, 200, 250, 95, 180, 170

I used the following steps to calculate the Five Number Summary. Please note that the method I use for calculating quartiles is only one of many different methods that can be used.

Sort Data Set In Descending Order

PositionValue
159
270
390
495
5100
6130
7130
8150
9150
10170
11180
12200
13200
14200
15200
16220
17250
18250
19270
20275
21300
22325
23350
24400
25400
26450

Find the Minimum and Maximum

Based on the table above, the minimum value in the data set is 59, and the maximum value in the data set is 450.

Find the 1st Quartile (Lower)

To find the position of the 1st quartile (lower), we solve for the following equation, where n is equal to the number of values in the set (26):

Q1 Position= 0.25(n + 1)
 = 0.25(26+ 1)
 = 0.25 x 27
 = 6.75

Since 6.75 is not an integer, we can use interpolation to find the 1st quartile that is located somewhere between the values located at the 6th and 7th positions, which are 130 and 130, respectively.

Step #1: Find the difference between the two values between which Q1 is located:

130 - 130 = 0

Step #2: Get the decimal part of the Q1 position and multiply it by the result in step #1:

0.75 x 0 = 0

Step #3: Add the result in step # 2 to the smallest number in step #1:

0 + 130 = 130

Q1 = 130

Find the Median (Middle)

To find the position of the middle value we solve for the following equation, where n is equal to the number of values in the set (26):

Median Position= 0.50(n + 1)
 = 0.50(26+ 1)
 = 0.50 x 27
 = 13.5

Since 13.5 is not an integer, we can use interpolation to find the median that is located somewhere between the values located at the 13th and 14th positions, which are 200 and 200, respectively.

Step #1: Find the difference between the two values between which Q1 is located:

200 - 200 = 0

Step #2: Get the decimal part of the median position and multiply it by the result in step #1:

0.5 x 0 = 0

Step #3: Add the result in step # 2 to the smallest number in step #1:

0 + 200 = 200

Median = 200

Find the 3rd Quartile (Upper)

To find the position of the 3rd quartile, we solve for the following equation, where n is equal to the number of values in the set (26):

Q3 Position= 0.75(n + 1)
 = 0.75(26+ 1)
 = 0.75 x 27
 = 20.25

Since 20.25 is not an integer, we can use interpolation to find the 1st quartile that is located somewhere between the values located at the 20th and 21st positions, which are 275 and 300, respectively.

Step #1: Find the difference between the two values between which Q1 is located:

300 - 275 = 25

Step #2: Get the decimal part of the Q3 position and multiply it by the result in step #1:

0.25 x 25 = 6.25

Step #3: Add the result in step # 2 to the smallest number in step #1:

6.25 + 275 = 281.25

Q3 = 281.25

Below are the color-coded results of my 5 Number Summary calculations for the entered set of data, followed by my attempt to create a rough visual presentation of the summary (hopefully somewhat similar to an official Box and Wisper Plot).

5 Number Summary
Minimum59
Q1 (Lower)130
Median (Middle)200
Q3 (Upper)281.25
Maximum450
500 -
410 -
320 -
230 -
140 -
Back to CalculatorBack to CalculatorBack to 5 Number Summary CalcBack up to Five Number Summary Calculator

Adjust Calculator Width:

Move the slider to left and right to adjust the calculator width. Note that the Help and Tools panel will be hidden when the calculator is too wide to fit both on the screen. Moving the slider to the left will bring the instructions and tools panel back into view.

Also note that some calculators will reformat to accommodate the screen size as you make the calculator wider or narrower. If the calculator is narrow, columns of entry rows will be converted to a vertical entry form, whereas a wider calculator will display columns of entry rows, and the entry fields will be smaller in size ... since they will not need to be "thumb friendly".

Show/Hide Popup Keypads:

Select Show or Hide to show or hide the popup keypad icons located next to numeric entry fields. These are generally only needed for mobile devices that don't have decimal points in their numeric keypads. So if you are on a desktop, you may find the calculator to be more user-friendly and less cluttered without them.

Stick/Unstick Tools:

Select Stick or Unstick to stick or unstick the help and tools panel. Selecting "Stick" will keep the panel in view while scrolling the calculator vertically. If you find that annoying, select "Unstick" to keep the panel in a stationary position.

If the tools panel becomes "Unstuck" on its own, try clicking "Unstick" and then "Stick" to re-stick the panel.