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Measures Of Spread

Range
This is the simplest measure of spread - the difference between the largest and the smallest value in the data set.

Range = largest - smallest

Mid-range
Don't get this and the range confused - the midrange is the largest and smallest value added together and divided by 2.

The Mean Absolute Deviation

Sum of Squares

The sum of squares is pretty easy to work out once you've done the steps in the video above. All you need to do is square all the numbers in the last column of the table in the bottom left of the video. This means squaring 5, 12, 10, 17, 15 and 5. You should get 25, 144, 100, 289, 225. Then as it's the 'sum of squares' just add up all those numbers you've squared. You should get 783. This is your sum of squares.

The Mean Square Deviation and Root Mean Square Deviation
All the mean square deviation (msd) is is the sum of squares we worked out above, divided by the number of numbers there is in the data set. Look at the example above, this would be:

msd = ⁷⁸³ ⁄ ₅
= 156.6

The root mean square deviation is also quite simple - it's just the square root of what we've calculated above (√msd):

√156.6 = 12.5 (1 decimal place)

The Variance and Standard Deviation
To find the variance, we just take the sum of squares and divide it by n - 1 - it's basically the same as the msd but we're dividing by n - 1 instead of just n. We call the variance s². Lets use the example above again:

Sum of squares = 783. s² = ⁷⁸³ ⁄ _{n - 1}
⁷⁸³ ⁄ _{5 - 1}
⁷⁸³ ⁄ ₄
= 195.75

The standard deviation is just the sqaure root of the variance - as it is symbolised as just s.

s = √195.75
s = 14.0 (1 decimal place)

The Standard Deviation and Outliers
Sometimes data sets have extreme values in them which can cause problems. In statistics, we usually say that if a certain value s more than two standard deviations away from the mean, it should be investigated as it might be a possible outlier. If it is over three standard deviations away from the mean then the case is even stronger. This test is one of several different ways we can identify possible outliers, but this is what you mainly use - or sometimes just initiative.