© 1999 Prentice-Hall, Inc. Chap Measures of Central Location Mean, Median, Mode Measures of Variation Range, Variance and Standard Deviation Measures of Association Covariance and Correlation Describing Data: Summary Measures

© 1999 Prentice-Hall, Inc. Chap It is the Arithmetic Average of data values: The Most Common Measure of Central Tendency Affected by Extreme Values (Outliers) Mean = 5Mean = 6 Sample Mean Mean n xxx n2i   n x n 1i i    x

© 1999 Prentice-Hall, Inc. Chap Median = 5 Important Measure of Central Tendency In an ordered array, the median is the “middle” number. If n is odd, the median is the middle number. If n is even, the median is the average of the 2 middle numbers. Not Affected by Extreme Values Median

© 1999 Prentice-Hall, Inc. Chap Mode = 9 A Measure of Central Tendency Value that Occurs Most Often Not Affected by Extreme Values There May Not be a Mode There May be Several Modes Used for Either Numerical or Categorical Data No Mode Mode

© 1999 Prentice-Hall, Inc. Chap Variation VarianceStandard DeviationCoefficient of Variation Population Variance Sample Variance Population Standard Deviation Sample Standard Deviation Range Measures Of Variability

© 1999 Prentice-Hall, Inc. Chap Measure of Variation Difference Between Largest & Smallest Observations: Range = Ignores How Data Are Distributed: The Range Range = = Range = = 5 SmallestrgestLa xx 

© 1999 Prentice-Hall, Inc. Chap Important Measure of Variation Shows Variation About the Mean: For the Population: For the Sample: Variance For the Population: use N in the denominator. For the Sample : use n - 1 in the denominator.  N (X i    2 2        n XX s i

© 1999 Prentice-Hall, Inc. Chap Most Important Measure of Variation Shows Variation About the Mean: For the Population: For the Sample: Standard Deviation For the Population: use N in the denominator. For the Sample : use n - 1 in the denominator.  N X i    2    1 2     n XX s i

© 1999 Prentice-Hall, Inc. Chap Sample Standard Deviation For the Sample : use n - 1 in the denominator. Data: s = n = 8 Mean =16 Sample Standard Deviation= s  1 2     n XX i

© 1999 Prentice-Hall, Inc. Chap Comparing Standard Deviations Mean = 15.5 s = Data B Data A Mean = 15.5 s = Mean = 15.5 s = 4.57 Data C

© 1999 Prentice-Hall, Inc. Chap Coefficient of Variation Measure of Relative Variation Always a % Shows Variation Relative to Mean Used to Compare 2 or More Groups Formula ( for Sample):

© 1999 Prentice-Hall, Inc. Chap Comparing Coefficient of Variation Stock A: Average Price last year = $50 Standard Deviation = $5 Stock B: Average Price last year = $100 Standard Deviation = $5 Coefficient of Variation: Stock A: CV = 10% Stock B: CV = 5%

© 1999 Prentice-Hall, Inc. Chap Shape Describes How Data Are Distributed Measures of Shape: Symmetric or skewed Right-Skewed Left-SkewedSymmetric Mean =Median =Mode Mean Median Mode Median Mean Mod e