The range describes the full extent of dispersion of the results. It is also called the variation interval.

The range is the largest difference between the scores and is calculated as the difference between the highest and lowest scores in the distribution. It is calculated using the formula

Y = Xmax - Xmin

where

Y – the range designation,
Xmax – the largest element in the data set, and
Xmin – the smallest element in the data set

Since only the two extreme values are taken into account when calculating the range, the range is affected by extreme results and can create a false picture of the variability of the results.

If the range is calculated on a continuous variable, then one unit of measurement is added to the difference between the highest and lowest results. The addition of the unit of measure is done because of the actual upper limit of the interval of the highest score and the lower limit of the interval of the lowest score.

Example: Height range of girls in 52 class

In the example of the height of girls in 52 class of the "X" elementary school (in cm) that we used for the example of calculating the arithmetic mean, median and mode, we obtained the following data: 140, 141, 138, 140, 122, 160, 154, 132, 148, 135, 140.

We obtain the height range of girls in that class by subtracting the lowest result (122cm) from the highest result (160cm). Range=160-122=38.

Since height is a continuous variable, one unit of measurement is added to the difference, which in this case is one, so the range is 38 + 1 = 39. The upper limit of the result 160 is 160.5, and the lower limit of 122 is 121.5.

Answer: The height range of girls in the 52 class of the "X" elementary school is 39.