1. Mean and Standard Deviation
Probability
and
Statistics

2. Relationship: Population and Sample
Please Note: We are focusing on the statistics of a population.

3. Formula for the Mean (Average)
The mean, denoted µ, of samples x1, x2, …, xn is the average of the values:
This formula can also be written as:

4. Formula for Standard Deviation
The standard deviation, denoted σ, of samples x1, x2, …, xn is the variation from the mean of those samples.
Formula:

5. Example Problem
The ages of a random sample of college students was collected and are as follows:
18, 24, 18, 19, 22, 21, 19, 20, 24, 35, 19, 15, 20
Find the mean (average) for this collection of ages.
Find the standard deviation of the values.

6. Solution (Part 1) The mean of the values:
(18, 24, 18, 19, 22, 21, 19, 20, 24, 35, 19, 15, 20)
is the sum of all of the values divided by the total number of values
The mean, µ = ( ) ≈ 21.08 13

7. Solution (Part 2) The standard deviation of the values: ≈ 4.86
(18, 24, 18, 19, 22, 21, 19, 20, 24, 35, 19, 15, 20)
is the square root of: [sum of (xi - µ)]2 / n
where n is the total number of values
≈ 4.86

8. Brief Review Given the same list of numbers:
18, 24, 18, 19, 22, 21, 19, 20, 24, 35, 19, 15, 20
Is there a mode among these values, and if so, what is it?
What is the median?
Are there any outliers that might possibly skew the data?