7.3 Measures of Central Tendency and Dispersion

Mean – the arithmetic average is the sum of all values in the data set divided by the number of values.

Median – the middle value when the data values are arranged in ascending or descending order. If there are an even # of values then

find the mean of the middle 2 values.

Mode – the value that is repeated most often from the data.

Can be 0, 1 or more than one modes

x

Measures of Central Tendency

Measures of DispersionMeasures of Dispersion

Standard Deviation: Symbol

Range: highest value – lowest value

How Spread Out

How Spread Out

sigma

Formula

2 2 21 2 ... nx x x x x x

n

When we talk about data, often times it falls on what we call a normal curvenormal curve.

This gives us a picture of how the Standard DeviationStandard Deviation can tell us how an individual value relates to the bulk of the data.

Find the , median, mode and range for the following data. 40, 45, 39, 40, 42,

41, 37, 41, 40, 41

x

40, 45, 39, 40, 42,41, 37, 41, 40, 41

Now let’s find the standard deviation.

n

xxxxxx n22

22

1 ...

ix ix x 2ix x

21

n

ii

x x

n