1. Measures of Central Tendency
The three measures in common use are the:
Mean
Median
Mode
Measures of Dispersion
Range
Standard Deviation
Variance

2. Statistics – ‘Mean’ Mean = arithmetic average = X bar (as spoken)
= X (as written)
= S X n
where S X = sum of X’s
and n = sample size

3. Example of a ‘mean’ value
Find the mean value of: 4,6,7,9,4.
= S X = X n 5
= 30 5
= 6

4. Statistics – ‘Median’ Median = middle value
Half of the values are greater than the median and half are less than the median, when the values are placed in numerical order.

5. Example of a ‘median’ value
Find the median value of: 4,6,7,9,4.
Put the numbers in numerical order:
4, 4, 6, 7, 9.
The middle number is the median:
The median number is 6

6. Statistics – ‘Mode’ Mode = most frequently occurring value
Find the mode of 4,6,7,9,4
The most popular, or mode is 4

7. Distribution Curves - location
For a Normal Distribution Curve:
The mean, median and mode all lie at the same point.

8. Statistics - Range Range = spread of the extreme results Example:
Find the range of 4,6,7,9,4,2,5,8,7,9,3
The extreme values are 2 and 9.
The range ‘R’ = 9 – 2 = 7

9. Variance and Standard Deviation
Instead of taking the absolute value, we square the deviations from the mean. This yields a positive value.
This will result in measures we call the Variance and the Standard Deviation
Sample Population-
s: Standard Deviation σ: Standard Deviation
s2: Variance σ2: Variance

10. Calculating the Variance and/or Standard Deviation
Formulae:
Variance:
Examples Follow . . .
Standard Deviation:

11. Example: Mean: -1 1 3 9 -2 4 -3 2 6 10 5 4 9 8 Variance:
Data: X = {6, 10, 5, 4, 9, 8}; N = 6
Mean: -1 1 3 9 -2 4 -3 2 6 10 5 4 9 8
Variance:
Standard Deviation:
Total: 42
Total: 28