The coefficient of variation, also known as the relative standard deviation compares the spread of data between two datasets. The Coefficient of Variation equals the standard deviation divided by the mean. Let’s take four siblings of different ages, the youngest being 1, the second youngest being 3, the second oldest being 7 and the oldest being 14, and calculate the coefficient of variation for this group’s age.
We begin by calculating the mean or average age of the group. This is done by adding the ages of the siblings together and dividing that sum by the total amount of children. This gives us an average or mean age of 6.25 years. Now we need to calculate the variance in age of the siblings as the variance is the standard deviation squared. The variance is calculated by subtracting the mean age, from the age of each child and squaring that difference. All these squared age differences are then summed together and finally divided by the total amount of siblings minus 1, which gives us a variance of 32.92 years. Now, we can simply take the square root of the variance to get the standard deviation, which is 5.74 years. Finally we divide the standard deviation, which is 5.74 years with the mean, which is 6.25 years, just like the formula states and convert the answer to a percentage. This gives us a coefficient of variation of 91.80%
But what does this mean? Well, if we were to compare these 4 siblings which have a coefficient of variation of 91.80% to another set of siblings that had a coefficient of variation of let’s say 50%, it would mean that the second set of siblings with the smaller coefficient of variation has a much smaller spread or variation in their ages. More simply put, it would mean that the second set of siblings are much closer in age to one another.
5 окт 2024
