Summary Measures Central Tendency Mean Median Mode Midrange Quartile Midhinge Summary Measures Variation Variance Standard Deviation Coefficient of Variation. - презентация

1 Summary Measures Central Tendency Mean Median Mode Midrange Quartile Midhinge Summary Measures Variation Variance Standard Deviation Coefficient of Variation Range

2 Measures of Central Tendency Central Tendency MeanMedianMode Midrange Midhinge

3 The Mean (Arithmetic Average) 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

4 The Median 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

5 The Mode 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

6 Midrange A Measure of Central Tendency Average of Smallest and Largest Observation: Affected by Extreme Value Midrange Midrange = 5

7 Quartiles Not a Measure of Central Tendency Split Ordered Data into 4 Quarters Position of i-th Quartile: position of point 25% Q1Q1 Q2Q2 Q3Q3 Q i(n+1) i 4 Data in Ordered Array: Position of Q 1 = 2.50 Q1Q1 =12.5 = 1(9 + 1) 4

8 Midhinge A Measure of Central Tendency The Middle point of 1st and 3rd Quarters Not Affected by Extreme Values Midhinge = Data in Ordered Array: Midhinge =

9 Measure of Variation Difference Between Largest & Smallest Observations: Range = Ignores How Data Are Distributed: The Range Range = = Range = = 5

10 Measure of Variation Also Known as Midspread: Spread in the Middle 50% Difference Between Third & First Quartiles: Interquartile Range = Not Affected by Extreme Values Interquartile Range Data in Ordered Array: = = 5

11 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.

12 Comparing Standard Deviations s = = = Value for the Standard Deviation is larger for data considered as a Sample. Data : N= 8 Mean =16

13 Comparing Standard Deviations Mean = 15.5 s = Data B Data A Mean = 15.5 s = Mean = 15.5 s = 4.57 Data C

14 Coefficient of Variation Measure of Relative Variation Always a % Shows Variation Relative to Mean Used to Compare 2 or More Groups Formula ( for Sample):

15 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%

16 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

17 Box-and-Whisker Plot Graphical Display of Data Using 5-Number Summary Median Q 3 Q 1 X largest X smallest

18 Distribution Shape & Box-and-Whisker Plots Right-SkewedLeft-SkewedSymmetric Q 1 Median Q 3 Q 1 Q 3 Q 1 Q 3