Box and whisker plots

Leon's class have been doing long jumps. Here is each student’s best result. Leon sorts the results from lowest to highest. Then he calculates the median that divides the jumps into two equal parts. Those two parts are divided again with the median for the shorter jumps, and the median for the longer jumps.

These three values that divide the jumps are called ‘quartile one,’ ‘quartile two — the median’, and ‘quartile three’. The longest jump is 451 centimetres, and the shortest is 210 centimetres. To make it clearer, we can draw a picture, a graph, of these values. First, draw a number line. Grade the number line from 200 to 500.

Mark the smallest value, also called the minimum: 210 centimeters. Then, mark the first quartile: 276 centimetres. And the second quartile: 339 centimetres, which is also the median for all the values. Finally, mark the third quartile: 399 centimetres. And so the largest value, also called the maximum, is 451 centimetres.

We have recorded all the values on the number line. Now we will draw a rectangle, a box, above the number line. Let quartile one be the left side of the box.. ..and quartile three, the right side of the box. Connect the left and right sides of the box with two horizontal lines. Now the box is ready.

Divide the box into two parts with a vertical line at the median’s value. Mark the minimum and maximum with additional vertical lines. Draw one horizontal line, going from the minimum line to the box ...and one horizontal line going from the maximum line to the box. The box spans 50% of all the results — the 50% that are the closest to the median. To the right of the box, on the line going to the maximum, 451, are the longest 25% of jumps.

The shortest 25% of jumps are on the left of the box, on the line going to the minimum, 210. The maximum value minus the minimum value, that is 451 minus 210, is called the spread, or range, for all the long jumps. The spread of the 50% of values closest to the median is shown by the width of the box. The width is quartile three minus quartile one — which is 399 minus 276. That is 123.

This spread is called the interquartile range. So, a box and whisker plot shows: The smallest value, the minimum value. The largest value, the maximum value. The three quartiles: quartile one, on the left of the box, quartile two, the line inside the box, and quartile three, on the right of the box. The width of the box shows the interquartile range and the ‘width of the box’ PLUS ‘the length of the two whiskers is the entire spread — the range.

Alright - so where is “mode and mean ” then? We have that in another movie, Leon... Oh...okay… hm.