Chapter 3 Notes

©2009 by S. Gramlich

Definitions and Formulas for Describing Data Numerically

! = Important Note

! These Notes are not meant to replace Reading. Read Chapter first.

3-2

Mean = average

population: μ = ΣX / N

sample: xbar = Σx / n

Median = middle #

Mode = most frequently occurring #

Midrange = (Max + Min) / 2

Mean from Frequency Table and Weighted Mean

xbar = Σ(f*cm)/ n

where class midpoint = cm = (lower class limit + upper class limit)/2

sample size = n = Σf

Skewness (see Chapter 2 Notes)

3-3

Range = hi - lo

Variance & Standard Deviation = how far away, on average, the other data points are from the mean

Variance (in squared units)

! Recommend using (Definitional) Formula 3-4 from the text

population σ² = Σ(X-μ)² / N

sample s² = Σ(x-xbar)² / (n -1)

the numerator Σ(x-xbar)² is called the Sum of Squared Deviations (SS)

the denominator (n-1) is called the degrees of freedom (df)

Standard Deviation (in singular units) is the square root of Variance

population (Greek lowercase Sigma) σ = √σ²

sample s = √s²

Variance/Standard Deviation for a Frequency Table

sample Variance= s^2 = Σ [f*(cm-xbar)^2] / (n-1)

where class midpoint = cm = (lower class limit + upper class limit)/2

sample size = n = Σf

sample Standard Deviation= s = square root of s^2

TECHNOLOGY

using StatCrunch:

for mean, variance, & standard deviation: Stat - Summary Stats - Columns - Select Column – Calculate

EXCEL commands:

! highlight the data you want to calculate inside the parentheses

Statistic Excel Command

Sum: =sum( )

Sample Size: =count( )

Minimum: =min( )

Maximum: =max( )

Mean: =average( )

sample Variance: =var( )

sample Standard Deviation: =stdev( )

Median : =median( )

Mode: =mode( )