Mean and Standard Deviation

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Presentation transcript:

Mean and Standard Deviation Probability and Statistics

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

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:

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

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.

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 = (18+24+18+ . . . +20) ≈ 21.08 13

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

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?