How to create boxplot with whiskers

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This tutorial was written by Henk van der Burg, Harry Croon, Rob Westein and Kees Kriek.

Introduction

A box plot is a graphical representation of a data set, showing:

   • The minimum (the lowest value).
   • The first quartile.
   • The median.
   • The third quartile.
   • The maximum (the highest value).

This data set can be, for example, a large database or a sample from a population.

The median

The median of an odd number of numbers is the value of the middle number of that row of numbers after the row is sorted by size. If the number of numbers is even, the average of the two middle numbers is taken.

Median for an even number of numbers in a number sequence

With an even number of numbers, the median is always between the 2 middle numbers. The median is then the mean of these two middle numbers. For example, we have the following numbers: 942-721-483-223-934-780-317-356. We first put these numbers from smallest to large, so 223-317-356-483-721-780-934-942. The median is between the 2 middle bold numbers and is then (483 + 721) / 2 = 602.

Median for an odd number of numbers in a number sequence

With an odd number of numbers, the median is the middle number. The middle, bold, number, the fifth, in the range 223-317-356-483-721-780-934-942-966 is the median.

The first and third quartiles

After we have determined the median, we can also calculate the quartiles. The median splits the data series into two parts, as it were, creating a left and a right part. The first quartile is the median of the left portion and the third quartile is the median of the right portion. These can be determined in the same way as explained above. So split the number sequence, 223-317-356-483-721-780-934-942-966. The first quartile in the bold left part of the number sequence is therefore between 317 and 356 in and is then (317 + 356) / 2 = 336.5. The third quartile in the italicized right part is between 780 and 934 and is then (780 + 934) / 2 = 857.

Im-jabber.svg

Note:
It should be clear from the above explanation that the differences between the minimum, 1st quartile, median, 3rd quartile and maximum are only equal if the numbers in the series are evenly (uniformly) distributed.

Draw a box plot with pen and paper

Now that we know what the median, the first and the third quartiles mean, we can start making a box plot. In a box plot we will further use the minimum and the maximum. You make a box plot as follows. First make a line with numbers in which the box plot should be placed. Then place a dot at the lowest value, the first quartile, the median, the third quartile and the highest value. Then draw a rectangle between the first and third quartiles and place a line in this rectangle at the height of the median. This is shown schematically in Figure 1.

Figure 1: Schematic representation of a box plot with an even distribution of the numbers
1 - Minimum (Q0)

2 - Bottom whisker
3 - First quartile (Q1)
4 - Median (Q2)
5 - Third quartile (Q3)
6 - Upper whisker
7 - Maximum (Q4)

Create Box Plots Using Calc

Calc does not currently have a prepared diagram to create a box plot, so we need to build a box plot using the above theory. As an example we will use Table 1, which shows the annual sales of the stores in 2018, 2019 and 2020.

Table 1: Monthly sales of stores in 2018 to 2020
A B C D
1 Stores 2018 2019 2020
2 Amhem 133 195 132
3 Rotterdam 117 199 100
4 Amsterdam 189 177 170
5 Den Haag 152 194 125
6 Hilversum 157 123 120
7 Harderwiik 119 120 121
8 Alkmaar 118 135 148
9 Woerden 100 194 162
10 Den Bosch 136 120 136
11 Groningen 112 135 113
12 Zwolle 149 185 121
13 Assen 110 183 107
14 Leeuwarden 172 156 176


   1) Copy the range A1:D14 from Table 1 to a blank Calc worksheet.
   2) Save this worksheet with the name BoxplotBranches.

Calculate the concepts mentioned in the Introduction

   1) Select and right click cells A16:D16 and select Merge Cells in the context menu or select Format ▸ Merge Cells on the main menu bar.
   2) Type the text Summary Minimum, Median, Maximum, 1st and 3rd quartiles.
   3) In cells A17, A18, A19, A20, and A21, type Minimum (Q0), First quartile (Q1), Median (Q2), Third Quartile (Q3), and Maximum (Q4).

Calculate the minimum

   1) To calculate the minimum over the year 2018, place the mouse pointer in cell B17, type the equal sign (=) and select the Function Wizard icon on the Formula Bar, which will open the Function Wizard dialog box Figure 2.
Figure 2: Function Wizard dialog box
   2) In the Functions list, double-click the MIN function, or from the Category list above it, first select Static, and then double-click the MIN function in the Functions list. In the Function Wizard, the right part is now filled with required field parameters (data) for the MIN function to be filled in with a blinking mouse pointer in the Number 1 box (shown (not blinking) in Figure 3).
Figure 3: Minimized Function Wizard with the selected range
   3) Select the Shrink icon at the right of the Number 1 field, and then select the cell range B2:B14. Your selection will be inserted into the smaller dialog box of the Function Wizard (Figure 4).
Figure 4: Fields for the parameters (data) for the MIN function
   4) Click the same icon again, now named Expand, and the cell range will be included in the Function Wizard dialog box in the Number 1 box with 100 in the top right of the Function result and the same number in the Result box above the Formula box (Figure 5). The Formula box displays the formula and click OK.
Figure 5: The formula created in the Function Wizard dialog box
   5) The result of the MIN function is now listed in cell B17 and the formula is in the Input line on the Formula Bar (Figure 6).
Figure 6: Worksheet with the result in B17 and the function in the Input line of the Formula Bar
   6) In the black-outlined cell B17, place the mouse pointer on the small black square at the bottom right until the mouse pointer changes shape (under Windows into a plus sign). Click and drag cell B17 to cell D17 to copy the function and result to cells C17 and D17.
   7) Save your document before continuing.
Im-jabber.svg

Note:
The cell range B2:B14 coming from cell B17 has been changed in cells C17 and D17 to C2:C14 and D2:D14, respectively. This is because the cell range in B17 is relative, that is, copying to the right will adjust the cell range of the columns, so from B to C and from C to D. Copying down will adjust the cell range of the row so if B17 is copied one cell down, the cell range becomes B3:B15. If these adjustments are not desired, the cell range must be made absolute by using the F4 function key. Pressing the F4 function key once changes the cell range B2:B14 to $B$2:$B$14, which means that neither the columns nor the rows are adjusted when copying. Pressing F4 twice only places the character $ in front of the row numbers, indicating that they are now absolute and will not be changed during copying. Pressing F4 three times places the $ character in front of the columns only, and pressing F4 four times returns the cell range to its original formatting.

If you are already familiar with Calc functions, you can also enter the formula =MIN(B2:B14) directly into the Input line on the Formula Bar and press ↵ Enter.

You can also enter the formula directly into a cell by double-clicking the cell (the mouse pointer flashes in that cell) and then typing =MIN(B2:B14) followed by ↵ Enter.

The result of cell B17 can also be calculated with another formula: =QUARTILE(B2:B14,0).


Calculate the first quartile

In the theory in the section "The first and third quartiles" it is indicated that the first quartile is the median of the left part of a number sequence sorted from lowest to highest. The seventh (bold) number in the sorted number sequence (100,110,112,117,118,119,133, 136, 149, 152, 157, 172, 189) is the median of the number sequence. The median of the left portion (100,110,112,117,118,119) is between 112 and 117 (bold). Its median is: (112 + 117) / 2 = 114.5. Calc has a function for this that calculates this from the number sequence: the function QUARTILE.EXC (excluding median). That function calculates the first quartile (K1) in cell B18. Using the Function Wizard as described in points 1 to 6 of section "Calculate the minimum" or by entering the formula directly in the Input line on the Formula Bar or directly in the cell as described in the Note after point 7 above. The function to enter is: = QUARTILE.EXC (B2:B14,1). The 1 after the number sequence indicates that the first quartile must be calculated. After entering the function in cell B18, copy this cell to cells C18 and D18, as described under point 6 of section "Calculate the minimum". The Summary, Minimum, Median, Maximum, 1st and 3rd quartiles section in your table should then look like Figure 7.

Figure 7: Table after calculation First quartile

{note| The first quartile can also be calculated with the function PERCENTILE.EXC. The function for this is: =PERCENTILE.EXC (B2:B14, 0.25).}}

Gnome-dialog-warning.svg

Warning:
In the current number sequence, the left and right portions next to the median have an even number of numbers, so the centers, the medians, of that left or right portions lie between the pairs of the two middle numbers. In those cases, the QUARTILE.EXC or PERCENTILE.EXC function should be used. If the left part and right part next to the median have an odd number of numbers then the function QUARTILE, QUARTILE.INC, PERCENTILE or PERCENTILE.INC is used.


Calculate the median

We have already indicated the outcome of the calculation in the first paragraph of the text. Calc has the function MEDIAN to calculate this. The function for cell B19 is: =MEDIAN (B2: 14), which is processed in the same way as indicated for the calculation of the minimum and first quartile. The table after the calculation of the medians is shown in Figure 8.

Figure 8: Table after calculating the median


Im-jabber.svg

Note:
The functions =QUARTILE(B2:B14,2), =QUARTILE.INC(B2:B14,2), QUARTILE.EXC(B2:B14,2), =PERCENTILE(B2:B14,0.5) and PERCENTILE.EXC(B2:B14,2) all give the same result as =MEDIAN(B2:B14).

Calculate the third quartile

The calculation for the third quartile is basically the same as the calculation for the first quartile, where the reference to the profile should not be 1 in this case but 3 and 0.75 in the case of the PERCENTILE.EXC function. The functions are as follows: =QUARTILE.EXC (B2:B14,3) or PERCENTILE.EXC(B2:B14,075). After calculating the third quartile, you have a table like Figure 9.

Figure 9: Table after calculating third quartile
Gnome-dialog-warning.svg

Warning:
In accordance with the remark in the Caution under section "Calculate the first quartile", for an even number of numbers in the number sequence to be calculated, the function QUARTILE.EXC or PERCENTILE.EXC is used. An odd number of numbers uses the QUARTILE, QUARTILE.INC, PERCENTILE, or PERCENTILE.INC function.


Calculate the maximum

The maximum is calculated in the same way as the minimum, but using the MAX function instead of the MIN function. The function for this in cell B21 is: =MAX(B2:B14) and copy this cell back to cells C21 and D21. All concepts for the box plots have now been calculated in Figure 10.

Figure 10: Table after calculating the maximum


Im-jabber.svg

Note:
The QUARTILE, QUARTILE.INC, QUARTILE.EXC, PERCENTILE.INC, and PERCENTILE.EXC functions with the proper parameters can return the same result as the MAX function.

Determine differences between the elements of the box plot

From the theory in the section "Draw a box plot with pen and paper" and Figure 1, it can be concluded that the differences between the above data elements must be calculated. We do this in a separate table labeled Differences for the boxes and whiskers in the merged cells A23:D23 with underneath in cells B24, C24 and D24 containing 2018, 2019 and 2020 respectively.

   1) Merge cells A23:D23 as indicated in point 1 of "Calculate the concepts mentioned in the Introduction" and in these merged cells type the text Differences for Boxes and Whiskers and press ↵ Enter.
   2) In cells B24, C24, and D24, type 2018, 2019, and 2020, respectively, and press Right Arrow or Tab ↹ after each entry in the cell.
   3) In cells A25, A26, A27, A28, and A29, respectively, type Minimum (Q0), First quartile (Q1) - Minimum (Q0), Median (Q2) - First Quartile (Q1), Third quartile (Q3) - Median (Q2 ) and Maximum (Q4) - Third 
      quartile (Q3) and press ↵ Enter after each entry in a cell.
   4) The minimum in cell B25 is equal to the minimum in cell B17. In cell B25 type = B17 as a reference to this cell and press Enter, or in cell B25 type =, click the mouse pointer in cell B17 and press ↵ Enter.
   5) In cell B26 you must fill in the difference between the First quartile (Q1) and the Minimum (Q0), otherwise write the difference between cells B18 and B17. In cell B26 type the formula = B18-B17 and press ↵ Enter to calculate this difference, or in cell B26 type = and click the mouse pointer in B18, then type the character - and click the mouse pointer in cell B17 and press ↵ Enter or use the Function Wizard to calculate the difference.
   6) The differences in cells B27, B28 and B29 are calculated in a similar manner. Since cell B26 contains relative references, the formulas for these cells can be copied down, as previously described in point 6 of section "Calculate the minimum". Select cell B26 and hover the mouse pointer over the small square at the bottom right of the cell and when the mouse pointer has changed shape, drag the cell down to cell B29.
   7) All cells in B25 to B29 contain relative references and can be copied to the right in the same way as under point 6 above to calculate the differences for the years 2019 and 2020. Select the cell range B25:B29 and hover the mouse pointer over the small square at the bottom right of the selection in cell B29, and if the mouse pointer has changed shape, drag the selection 2 columns to the right.
   8) The table now contains the data shown in Figure 11.
Figure 11: Table after calculating the differences
   9) Save the file.

Create the diagram

We are now going to make the diagram. Remember that the values in row 25 and row 29 are the bottom and top whiskers and these in B26 to B28 make up the boxes.

   1) Select cells B24:D29 and select Insert ▸ Chart on the main menu bar or click the icon Insert Chart on the Standard bar.
   2) Select Column from the Choose a Chart Type list in Step 1 of the Chart Wizard and select the middle example Stacked (see Figure 12).
Figure 12: Select a stacked column in Step 1 of the Chart Wizard
   3) Click Next.
   4) In Step 2 of the Chart Wizard, the checkbox for Data series in columns is selected, change it by clicking Data series in rows, also click First row as label to include the years in the chart (Figure 13) and click Next.
Figure 13: Step 2 of the Wizard Diagram
   5) In Step 3 of the Chart Wizard, do not change anything and click Next.
   6) In Step 4 of the Chart Wizard, deselect Display legend (Figure 14) and click Finish.
Figure 14: Step 4 of the Wizard Diagram
   7) Your diagram will now look like the one shown in Figure 15. Save your document.
Figure 15: The stacked columns for the boxes and the whiskers

Explanation of the colored blocks in the diagram

   • The tops of the blue stacks and the bottoms of the orange stacks are the bottoms of the bottom whiskers.
   • The tops of the orange stacks and the bottoms of the yellow stacks are the tops of the bottom whiskers.
   • The difference between tops and bottoms of the orange stacks make up the bottom whiskers.
   • The yellow and green stacks eventually form the box of the box plot.
   • The tops of the yellow stacks and the bottoms of the green stacks are the median in the box of the box plot.
   • The bottoms of the purple stacks are the bottoms of the top whiskers.
   • The tops of the purple stacks are the tops of the top whiskers.

The above is shown schematically for the 2018 column in Figure 16.

Figure 16: Schematic representation of column chart
1 - Bottom of bottom whisker

2 - Top of bottom whisker
3 - Median
4 - Bottom of top whisker
5 - Top of top whisker

Convert the stacked columns into a box plot with whiskers

Make the bottom whiskers in the diagram

Edit the blue blocks in the stacked column chart

The information above shows that only the tops of the blue stacks are important for determining the bottom whiskers. Also, the bottoms of the orange stacks are the same as the tops of the blue stacks. The blue stacks are therefore not really important when making the whiskers. We will therefore first remove the blue stacks from or make them invisible in the stacked columns.

   1) Double-click on the created diagram and a gray border appears around the diagram with a black block in the middle of all sides and at the corner points, a total of 8 pieces (see Figure 15).
   2) Then click in one of the blue blocks in the diagram. A small block (Figure 17) appears in the middle of these areas. (Note that when the mouse pointer reaches the blue block, a help tip is displayed that says: Data point x, data series x, values: Year x value.)
Figure 17: The small block with the help tip in the blue stack
   3) Now right click on one of the blue stacks and select Format Data Series in the context menu or select Format ▸ Format Selection on the main menu bar.
   4) The Data Series dialog box (Figure 18) opens. Click on the Area sheet tab to open the tab and select the None button (after which the block is no longer selectable) or select the Colour button and select the color White from one of the available palettes in the Colours section (after which the block is selectable and can still be changed). In the examples on the right side of the dialog box, the newly selected color is displayed under New.
Figure 18: Data Series dialog
   5) Then click the Borders sheet tab and select - none - as Style in the Line Properties section and click OK. All blue stacks are now no longer visible (Figure 19).
Figure 19: The stacked column chart without blue stacks

Edit the orange stacks in the stacked column chart

As indicated above, the bottom whiskers are formed by making the differences between the top and bottom sides of the orange areas in Calc (see also points 1 and 2 in Figure 16). The orange blocks themselves are therefore not required for making the bottom whiskers and they are removed or made invisible after the bottom whiskers have been applied. Proceed as follows:

   1) Double-click the stacked column chart if it does not have a gray border with 8 squares around it.
   2) Now select the orange stacks by clicking on one of the orange stacks. A small block will now appear in the orange stacks.
   3) Right-click on one of the orange stacks and select Insert y-Error Bars in the context menu or select Insert ▸ y-Error Bars on the main menu bar.
   4) The dialog box y-Error Bars for Data Series ‘Row 26’ opens. Click the Line sheet tab to open the Line tab, and in the Width field in the Line Properties section, change the value 0.00 cm to 0.03 cm (Figure 20).
Figure 20: y-Error Bars dialog box for Data Series, Line tab
   5) Now select the y-Error Bars sheet tab to open the y-Error Bars tab and select the Cell Range option in the Error Category section and Negative in the Error Indicator section. In the Parameters section, the Negative (-) box now becomes active.
   6) Click the Select data range button next to the Negative (-) box and select the cell range B26: D26 (Figure 21).
Figure 21: y-Error Bars dialog box for Data Series, y-Error Bars tab
   7) Click OK. Note, although difficult to see, that the whiskers are drawn in the diagram.
   8) Click again on one of the orange stacks (containing the small block) and eight square blocks are placed around the selected orange stack, the selection handles (Figure 22).
Figure 22: Selection handles around one of the orange stacks
   9) Right-click on the orange stack with the selected selection handles and select Format Data Series in the context menu.
   10) The Data Series dialog box opens. In it, delete the orange stack or make it invisible, as described in points 4 and 5 in the Edit the blue blocks in the stacked column chart section. This removes all orange stacks from the stacked column chart. Your diagram with the created bottom whiskers will now look like Figure 23.
Im-jabber.svg

Note:
In this situation, do not select Format ▸ Format Selection on the Menu bar. In this situation, only the selected stack will be edited and not all stacks.

Figure 23: The stacked column chart with the created whiskers and the removed orange stacks

Edit the yellow and green stacks in the stacked column chart

The yellow stacks in the stacked column chart make up the bottom parts of the boxes and the green top stacks make up the top parts of the boxes. The border between the yellow and green stacks indicates the median. To do this in Calc, do the following:

   1) Double-click on the stacked column chart so that it has a gray border with 8 black blocks around it (Figure 15).
   2) Click on one of the yellow stacks so that a small block appears in it and right-click on one of the yellow stacks and select Format Data Series in the context menu or select Format ▸ Format Selection on the main menu bar.
   3) Click the Borders sheet tab in the Data Series dialog box to open the Borders tab.
   4) Select Continuous from the Style drop-down list in the Line Properties section and change the Width to 0.03 cm. Leave the color of the stacks unchanged. See The color of the boxes in the box plots with whiskers. after this and click OK.
   5) The yellow stacks now have a black border around them.
   6) Carry out the same actions from points 2 to 4 on the green stacks, so that the box and the median are created in Figure 24.
Figure 24: The stacked column chart with the bottom whisker, box, and median

Edit the purple stacks in the stacked column chart

The purple stacks indicate the length of the top whiskers, which are drawn from the bottom to the top of the purple stacks. Since the bottom of the purple stacks is the same as the top of the green stacks, that information is not required. Our last table on row 29 determined the length of the top whiskers. The purple stacks are therefore not necessary (anymore) when making the box plots. Delete the purple stacks as described in points 1 to 5 under Edit the blue blocks in the stacked column chart. Your stacked column chart now looks like Figure 25.

Figure 25: The stacked column chart without the purple stacks

Make the top whiskers in the diagram

The top whiskers must be placed on top of the boxes, consisting of the yellow and green parts, and have the length calculated on row 29 of the table shown in Figure 11. Do the following to place the top whiskers.

   1) Double-click on the diagram so that it has a gray border with 8 black blocks around it (Figure 15).
   2) Click on one of the green stacks so that a small block appears in it (Figure 24).
   3) Right-click on one of the green stacks and select Insert y-Error Bars in the context menu or select Insert ▸ y-Error Bars on the main menu bar to open the dialog y-Error Bars for given ‘Row 28’.
   4) Click the Line sheet tab and choose Continuous from the Style drop-down list in the Line Properties section of this tab and change the Width to 0.03 cm.
   5) Click the y-Error Bars sheet tab and click Cell Range in the Error Category section and Positive in the Error Indicator section to select these parameters.
   6) Click the Select data range icon to the right of the Positive (+) box in the now active Parameters section.
   7) Select the cell range B29:D29 in the last table. The cell range is now included in the dialog y-Error Bars for data ‘Row 28’ (Figure 26).
Figure 26: Y Error Bars dialog box for data series, Y Error Bars tab
   8) Click OK and the top whiskers have been created in the diagram and your box plots and whiskers are complete (see Figure 27) and save the document.
Figure 27: The full box plots with whiskers created from the stacked column chart

The color of the boxes in the box plots with whiskers

In our box plots with whiskers, the boxes are indicated by yellow stacks below the median (the middle lines in the boxes) and by green stacks above the median. In many cases, no color is given to the surfaces, which makes them appear white. Excel 2016 and Excel 2019, where a box plot with whisker is one of the standard diagrams, the boxes per column (in our diagram the columns 2018, 2019 and 2020) are given a separate color, so that visually the difference in columns is visible. Depending on your preference or the situation in which you are going to use the box plots with whiskers, you can choose one of the above options. To adjust the colors in the boxes of the box plots:

   1) Double-click on the diagram so that it has a gray border with 8 black squares around it.
   2) To make all stacks white, select one of the yellow or green stacks and right-click on one of the yellow or green stacks and select Format Data Series in the context menu or select Format ▸ Format Selection on the main menu bar.
   3) On the Area tab of the Data Series dialog box, select the None button or the Colour button and choose White from the palettes in the Colours section.
   4) To white or color only the stack in the 2018 column, click the yellow or green stack in the 2018 column so that it has selection handles around it and select Format Data Point in the context menu or select Format ▸ Format Selection on the menu bar. Click the Colour button and choose the color White or the color of your choice from one of the palettes in the Colours section and click OK.
   5) Make the other parts of the box the same as the choices made above. A possible example is shown in Figure 28.
Figure 28: Example of formatted boxes in the block spots

Summary

If the box plots with whiskers are placed next to the stacked column charts, as in Figure 29, in the box plots it seems easier to observe that there is a reasonable skewed growth between the years 2018 to 2020 than in the stacked column charts.

Figure 29: Box plots and stacked column charts side by side

It is also easier to see in the box plots that the average over the year is fairly evenly distributed for the year 2018. For the year 2019, the average is well above it and for the year 2020 the average is well below it.