Math Assignment Help With Measures of Variability

10.3 Measures of Variability:

Variability refers to the spread or dispersion of scores. A distribution of scores is said to be highly variable if the scores differ widely from one another.

Consider the following two sets of scores:

Set A: 4, 5, 6, 7, 8

Set B: 2, 4, 6, 8, 10

We can see that the means for these two sets of scores are the same:

For Set A the mean is (4 + 5 + 6 + 7 + 8)/5 = 6

For Set B the mean is (2 + 4 + 6 + 8 + 10)/5 = 6

Although these two sets of scores have the same mean, they differ in how much the scores are spread out. The scores in Set A vary over a smaller set of values (4 through 8) than does Set B which varies over score values from 2 through 10.

10.3.1 Range: The difference between the lowest and highest values.

In {4, 6, 9, 3, 7} the lowest value is 3, and the highest is 9, so the range is 9-3 equals 6.

Range can also mean all the output values of a function.

Range = Highest Score - Lowest Score + 1

For Set A the Range = (8 - 4) + 1 = 4 + 1 = 5

For Set B the Range = (10 - 2) + 1 = 8 + 1 = 9

As we expected the set of scores with the greater spreadoutedness (Set B), has a larger range than the set with less variability (Set A).

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