3.3 Finding the Standard Deviation of a Data Set Theory

Variance

(1) how data is spread out

3 Ways to Measure Variation

(1) range

(2) standard deviation

(3) variance

Range

(1) the range of numbers

Formula for Range

Range = Max Value - Min Value

What is standard deviation?

(1) distance from the mean

3 Properties of Standard Deviation

(1) never negative

(2) never zero

(3) greatly affected by outliers

Variable for Sample Standard Deviation

s

Variable for Population Standard Deviation

S

2 Formulas for Sample Standard Deviation

Formula for Population Standard Deviation

Table for Formula 1 Standard Deviation

Table for Formula 2 Standard Deviation

How do you find the variance?

(1) square standard deviation

Sample Variance Formula

s = s²

Population Variance Formula

V = σ²

Small standard deviation means…

(1) closely grouped data

Large standard deviation means…

(1) spread out data

When does the empirical rule work?

(1) when data is normal

Empirical Rule

(1) 68% of data will fall within one standard deviation

(2) 95% of data will fall within two standard deviations

(3) 99.7% of data will fall within three standard deviations

How many standard deviations does usual data lie?

(1) 1 to 2

How many standard deviations does unusual data lie?

(1) 3 up

Steps to Finding the Number of Standard Deviations Away from the Mean

Step 1: Find the distance between the mean and the given endpoint data values, subtract the “lower limit” from the mean and the “higher limit” from the mean respectively, do each side separately

Step 2: Divide that number by the standard deviation

Formula for Number of Standard Deviations Away from the Mean

What is coefficient of variation?

(1) compares the standard deviation from the mean by taking the ratio and converting to percentage

Coefficient of Variation Formula