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Measures of Variability

In this lesson we learn the concept of  variability  and how to compute three measures of the variability of a data set.

Let’s start with two data sets:

Data set 1: 10,8,12,10,9,13,10,9,10

Data set 2: 16,7,10,3,12,6,10,17,4,15

The mean, median and mode of both data sets is the same: 10

The range is the difference between the largest and the smallest value in the data set.

For Data set 1 the range is 13-8=5 and for the second is 17-3=14

The range indicates the size of the smallest interval which contains all the data.  Less variability means a smaller range.

Since the range is based solely on the two most extreme values within the data set, if one of these is either exceptionally high or low (outlier) it will result in a range that is not typical of the variability within that data set.

The sample variance for data set 1 is 2.1 and for the second data set is 22.4

The sample standard deviation is 1.5 for the first data set and 5 for the second data set

Decimal Multiplication

Suppose you want to multiply 25.3 by 0.46.
Pretend that you’re multiplying numbers without decimal points:
Now you need to find out where the decimal point goes.
To do this, notice that 25.3 has one digit after the decimal point, and that 0.46 has two digits after the decimal point.
Place the decimal point in the answer so that it has three digits after the decimal point.