シナジーのメタファー４

3 Easy statistical processing

3.1 Variations of data

If we took a group A (5, 5, 5, 5, 5), group B (3, 4, 5, 6, 7) and group C (1, 3, 5, 7, 9), the arithmetic average would be 5 and the median value also 5. If these three groups were based on the arithmetic average and median value as representative value, they would be the exact same. But obviously if we consider variations, there is a difference.
Group A is all 5, therefore there is no variation. In group B 5 is in the middle, therefore there are variations between 3 and 7. Group C has a broader range of variations between 1 and 9. Group B is smaller than group C in terms of variations.
If we additionally consider group D (1, 1, 4, 7, 7) and group E (1, 4, 4, 4, 7), which group is bigger in terms of variations? Group D has four values at a point distant from the center 4. Group E has three values in the center and two values around that.
The range and standard deviation are the most common methods to define the size of variations. Range is found by subtracting the maximum from the minimum in a group. Group D’s range is 6 (7-1=6) and group E is also 6 (7-1=6). If we were to define the variations only by the range here, group D and group E are identical. However, since this only concerns the maximum and the minimum, all other values are ignored. Let’s examine the other common variation method called the standard deviation below.

花村嘉英（2017）「日本語教育のためのプログラム」より英訳 translated by Yoshihisa Hanamura