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Hanze University of
         Applied Science
         Groningen
Ning Ding, PhD
Lecturer of International Business
School (IBS)
n.ding@pl.hanze.nl
What we are going to learn?
• Review

• Chapter 3: Dispersion
   •   Range
   •   Variance (SD2)
   •   Standard Deviation (SD)
   •   Coefficient of variation (CV)


• Chapter 4: Displaying and exploring data
   • Dotplot
   • Stem-leaf
   • Boxplot
   • Skewness
Review

                              a                             b
Review

Chapter 3:
                      Discrete counting      Continuous measuring
Dispersion
–Range
–Variance (SD2)
–Standard Deviation
 (SD)
–Coefficient of
 variation (CV)


Chapter 4:
Displaying and               1.Age              5. Salary
exploring data
–Dotplot
–Stem-leaf
                             2.Sales volume     6. Class size
–Boxplot
–Skewness                    3. Temperature     7. Height

                             4. Weight          8. Shoe size (NL)
Review
     Constructing Frequency Distribution: Quantitative Data




 a. 4    b.5   c.6    d.70

 25 = 32, 26 = 64, suggests 6 classes
                                           Use interval of 100
 a. 80    b.100      c.120   d.150


i>        571- 41            = 88.33
            6
                                                        P46. N.30 Ch.2
Review




0       Cumulative
                     Class interval = 100
        relative
         relative




                                            P46. N.30 Ch.2
Central Tendency : Mean, Mode, Median
Mean: Average

        SCCoast, an Internet provider in the Southeast, developed the
        following frequency distribution on the age of Internet users.
        Describe the central tendency:




             X = 2410 / 60 = 40.17 (years)
                                                          P87 N.60 Ch.3
Review
            Central Tendency : Mean, Mode, Median
Mean: Average     Mode: Most Frequency

        SCCoast, an Internet provider in the Southeast, developed the
        following frequency distribution on the age of Internet users.
        Describe the central tendency:




            Mode = 45 (years)

                                                          P87 N.60 Ch.3
Review
                Central Tendency : Mean, Mode, Median
    Mean: Average     Mode: Most Frequency       Median: Midpoint

            SCCoast, an Internet provider in the Southeast, developed the
            following frequency distribution on the age of Internet users.
            Describe the central tendency:


a.40.25
b.41.25
c.30.50
d.37.50




                 Median = ? (years)
                                                              P87 N.60 Ch.3
Review

Step 1: Define the location of the median     Step 2: Calculate the median
                                                                    M
 Lm=(60+1)/2=30.5                              Value:40                         50
                                            Location: 28                        48


                                                                 30.5


                                                     30.5-28            M-40
                                                                =
                                                      48-28             50-40



                                                           Median= 41.25


                                                                        P87 N.60 Ch.3
Dispersion

Review
                      Range
Chapter 3:
Dispersion
–Range
–Variance (SD2)
–Standard Deviation
 (SD)
                      Variance (SD2) and Standard Deviation (SD)
–Coefficient of
 variation (CV)


Chapter 4:
Displaying and
                      Interquartile Range
exploring data
–Dotplot
–Stem-leaf
–Boxplot              Coefficient of variation (CV)
–Skewness
Dispersion

Review
                      – tells us about the spread of the data.
Chapter 3:
                      – Help us to compare the spread in two or more
Dispersion              distributions.
–Range
–Variance (SD2)
–Standard Deviation
 (SD)
–Coefficient of
 variation (CV)


Chapter 4:
Displaying and
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness
Dispersion: Range

Review                 Range:
Chapter 3:             is the difference between the largest and
Dispersion
–Range                 the smallest value in a data set.
–Variance (SD2)
–Standard Deviation
 (SD)
–Coefficient of
 variation (CV)
                      Example:
Chapter 4:
Displaying and        To find the range in 3,5,7,3,11
exploring data
–Dotplot
–Stem-leaf                            Range = 11-3 = 8
–Boxplot
–Skewness
Dispersion: Variance

Review
                       Population Variance:
                       • is the mean of the squared difference between each
Chapter 3:
Dispersion               value and the mean.
–Range                 • overcomes the weakness of the range by using all the
–Variance (SD2)
–Standard Deviation      values in the population.
 (SD)
–Coefficient of
 variation (CV)                            Σ(X - μ) 2
                                      σ2 =
Chapter 4:                                    N
Displaying and
exploring data
–Dotplot
–Stem-leaf
                      Sample Variance:
–Boxplot

                                              Σ(X - X) 2
–Skewness

                                         s2 =
                                                n -1
EXAMPLE – Variance Variance
                      Dispersion: and Standard
             Deviation
                              Population Variance:                     Σ(X - μ) 2
                                                                  σ2 =
Review                                                                    N
                 The number of traffic citations issued during the last five months in
Chapter 3:
Dispersion
                   Beaufort County, South Carolina, is 38, 26, 13, 41, and 22. What
–Range             is the population variance?
–Variance (SD2)
–Standard Deviation     Step 2: Find the difference between each observation and the mean
 (SD)
–Coefficient of
 variation (CV)


Chapter 4:
Displaying and                                                             Step 1: Get the mean
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness




                       Step 3: Square the difference and sum up          Step 4: Divided by N

   27
Dispersion: Standard Deviation

Review

Chapter 3:
Dispersion
                        Population Standard Deviation:
–Range
–Variance (SD2)
                        is the square root of the population variance.
–Standard Deviation

                                    σ=      σ2
 (SD)
–Coefficient of
 variation (CV)


Chapter 4:
Displaying and
exploring data
–Dotplot                Sample Standard Deviation:
–Stem-leaf
–Boxplot                is the square root of the sample variance.
–Skewness


                                   s = s2
Dispersion: Standard Deviation
                      Example:
Review                The hourly wages earned by a sample of five students are:
                               €7, €5, €11, €8, €6.
Chapter 3:
Dispersion            Find the variance and standard deviation.
–Range
                           Step 1: Get the mean         ΣX 37
–Variance (SD2)                                      X=    =   = 7.40
–Standard Deviation
 (SD)
                                                         n   5
                                                                   2
                                                           Σ(X - X )
                                                                                2                2
–Coefficient of
                           Step 2: Sum up the                          (7 - 7.4) + ... + (6 - 7.4)
 variation (CV)
                           squared differences        s2 =           =
                                                             n -1                 5 -1
Chapter 4:
                                                           21.2
Displaying and
                                                         =       = 5.30
exploring data
–Dotplot
                           Step 3: Divided by N-1          5 -1
–Stem-leaf
–Boxplot
–Skewness                  Step 4: Square root it    s = €2.30

                         The variance is €5.30;       the standard deviation is €2.30.
Dispersion: Standard Deviation

Review

Chapter 3:
Dispersion
                                         Compare
–Range
–Variance (SD2)
–Standard Deviation
 (SD)
–Coefficient of         20 40 50 60 80         20 49 50 51 80
 variation (CV)


Chapter 4:
Displaying and
                                                    Step 1: Get the mean
exploring data
–Dotplot
–Stem-leaf                                          Step 2: Sum up the
–Boxplot
                                                    squared differences
–Skewness



                                                    Step 3: Divided by N-1


                                                    Step 4: Square root it
Dispersion: Standard Deviation

Review

Chapter 3:
Dispersion
                                         Compare
–Range
–Variance (SD2)
–Standard Deviation
 (SD)
–Coefficient of         20 40 50 60 80         20 49 50 51 80
 variation (CV)


Chapter 4:
Displaying and
exploring data                                      •The sales of
–Dotplot
–Stem-leaf                                          MANGO is more
–Boxplot
–Skewness                                           closely clustered
                                                    around the mean
                                                    of 50 than the
                                                    sales of ZARA.
Dispersion: Standard Deviation

Review

Chapter 3:
Dispersion
–Range
–Variance (SD2)
–Standard Deviation
 (SD)
–Coefficient of
 variation (CV)


Chapter 4:
Displaying and
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness




   The standard deviation decreases because the new value 20 is very close to
   the mean 20.36.
Dispersion: Standard Deviation

Step 1:                  Step 3: Use f * (Mid-Mean)2
Find the Midpoint

Step 2:
Calculate the Mean




                                         P87 N.60 Ch.3
Dispersion: Standard Deviation




Step 4:
Calculate the Variance



Step 5:
Calculate the Standard Deviation

                                    P87 N.60 Ch.3
Dispersion: Coefficient of Variation

Review
                        Coefficient of Variation:
Chapter 3:              describes the magnitude sample values and the variation within
Dispersion              them.
–Range
–Variance (SD2)
–Standard Deviation
 (SD)
–Coefficient of
 variation (CV)
                      The following times were recorded by the quarter-mile and mile runners of a
Chapter 4:            university track team (times are in minutes).
Displaying and
exploring data        Quarter-Mile Times:           0.92      0.98     1.04     0.90      0.99
–Dotplot
–Stem-leaf            Mile Times:                   4.52      4.35      4.60       4.70      4.50
–Boxplot              After viewing this sample of running times, one of the coaches commented that
–Skewness
                      the quarter milers turned in the more consistent times. Calculate the appropriate
                      measure to check this and comment on the coach’s statement.
                      We can compare the dispersion with the coefficient of variation because they
                      have different “magnitudes”.
Dispersion: Coefficient of Variation


  Quarter-Mile Times:   0.92   0.98   1.04   0.90   0.99
  Mile Times:           4.52   4.35   4.60   4.70   4.50
Dispersion: Coefficient of Variation
                      The following times were recorded by the quarter-mile and mile runners of a
Review                university track team (times are in minutes).
Chapter 3:
                      Quarter-Mile Times:           0.92      0.98     1.04     0.90      0.99
Dispersion
                      Mile Times:                   4.52      4.35      4.60       4.70      4.50
–Range
–Variance (SD2)       After viewing this sample of running times, one of the coaches commented that
–Standard Deviation   the quarter milers turned in the more consistent times. Calculate the appropriate
 (SD)                 measure to check this and comment on the coach’s statement.
–Coefficient of
 variation (CV)       We can compare the dispersion with the coefficient of variation because they
                      have different “magnitudes”.
Chapter 4:
Displaying and
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness



                           No, the mile-time team showed more consistent times.
Displaying and Exploring Data

Review                 Dot plots:
Chapter 3:
Dispersion
–Range
–Variance (SD2)
–Standard Deviation
 (SD)
–Coefficient of
 variation (CV)


Chapter 4:
Displaying and
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness
Displaying and Exploring Data

Review                  Stem-and-Leaf Displays:
Chapter 3:              Each numerical value is divided into two parts. The leading
Dispersion
–Range
                        digit(s) becomes the stem and the trailing digit the leaf. The
–Variance (SD2)         stems are located along the vertical axis, and the leaf values are
–Standard Deviation
 (SD)                   stacked against each other along the horizontal axis.
–Coefficient of
 variation (CV)


Chapter 4:
Displaying and
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness




                                    Stem
Displaying and Exploring Data
                      Stem-and-Leaf Displays:
Review

Chapter 3:
Dispersion
–Range
–Variance (SD2)
–Standard Deviation
 (SD)
–Coefficient of
 variation (CV)


Chapter 4:
Displaying and
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness
Displaying and Exploring Data

Review                Quartiles, Deciles, and Percentiles
Chapter 3:
                      Alternative ways of describing spread of data include determining
Dispersion                the location of values that divide a set of observations into equal
–Range                    parts.
–Variance (SD2)
–Standard Deviation
 (SD)
–Coefficient of
 variation (CV)


Chapter 4:
Displaying and
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness
Displaying and Exploring Data

Review
                       Quartiles, Deciles, and Percentiles
Chapter 3:
Dispersion
–Range
–Variance (SD2)
–Standard Deviation
 (SD)
–Coefficient of
 variation (CV)


Chapter 4:
Displaying and
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness
Displaying and Exploring Data

Review
                      Quartiles, Deciles, and Percentiles
Chapter 3:
Dispersion                Raw                 Percentile
–Range
                          Score   Frequency   Frequency    Rank
–Variance (SD2)
–Standard Deviation
 (SD)                     95          1           25       100
–Coefficient of           93          1           24        96
 variation (CV)
                          88          2           23        92
Chapter 4:                85          3           21        84
Displaying and
exploring data            79          1           18        72
–Dotplot                  75          4           17        68
–Stem-leaf
–Boxplot                  70          6           13        52
–Skewness                 65          2            7        28
                          62          1            5        20
                          58          1            4        16
                          54          2            3        12
                          50          1            1         4
                                  N = 25
Displaying and Exploring Data

Review
                      Quartiles, Deciles, and Percentiles
Chapter 3:
Dispersion
–Range
–Variance (SD2)
–Standard Deviation
 (SD)
–Coefficient of
 variation (CV)         Example:
Chapter 4:
Displaying and                        101      43    75    61    91   104
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness
                                            The first quartile is ?
Displaying and Exploring Data

Review

Chapter 3:            Step 1:    Organize the data from lowest to largest value
Dispersion
–Range                                          101   43   75   61 91 104
–Variance (SD2)
–Standard Deviation
                                                      P1   P2   P3 P4 P5    P6
 (SD)
–Coefficient of
 variation (CV)       Step 2:                                                P1.75
Chapter 4:
Displaying and
exploring data
                      Step 3:    Draw two lines
–Dotplot
–Stem-leaf
–Boxplot
–Skewness        43                61-43 = 18              61


                 P1             0.75                       P2
Displaying and Exploring Data

Review

Chapter 3:
Dispersion
–Range
–Variance (SD2)
–Standard Deviation
                              Step 3:        Draw two lines
 (SD)
–Coefficient of
 variation (CV)                                43+13.5 = 56.5
Chapter 4:
Displaying and               43                  61-43 = 18           61
exploring data
–Dotplot
–Stem-leaf
–Boxplot
                             P1              0.75 * 18 = 13.5         P2
–Skewness


                                        The first quartile is 56.5.
Displaying and Exploring Data
  Listed below, ordered from smallest to largest, are the number
  of visits last week.




  a. Determine the median number of calls.
          a. 57median is 58.
           The   b.58 c.59        d.56

  b. Determine the first and third quartiles.
           Q1 = 51.25    Q3 = 66.00


    a. 50.25   b.51.25     c.60.00 d.62.25   e.63.00   f. 66.00




                                                       P110. N.14 Ch.4
Displaying and Exploring Data
  Listed below, ordered from smallest to largest, are the number of
  visits last week.




  c. Determine the first decile and the ninth decile.
           D1 = 45.30     D9 = 76.40

  d. Determine the 33rd percentile.
           P33 = 53.53




                                                       P110. N.14 Ch.4
Displaying and Exploring Data

Review
                      Box Plots
                      A graphical display, based on quartiles to visualize a set of data.
Chapter 3:
Dispersion
–Range
                              minimum       Q1       Median        Q3       maximum
–Variance (SD2)
–Standard Deviation
 (SD)
–Coefficient of
 variation (CV)


Chapter 4:
Displaying and
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness
Displaying and Exploring Data

Review
                      Box Plots
                      A graphical display, based on quartiles to visualize a set of data.
Chapter 3:
Dispersion
–Range
–Variance (SD2)
–Standard Deviation    minimum       Q1       Median        Q3       maximum
 (SD)
–Coefficient of
 variation (CV)


Chapter 4:
Displaying and
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness
Displaying and Exploring Data

Review

Chapter 3:
Dispersion
–Range
–Variance (SD2)
–Standard Deviation
 (SD)
–Coefficient of
 variation (CV)


Chapter 4:
Displaying and          Zero skewness      positive skewness      negative skewness
exploring data
–Dotplot              mode=median=mean   Mode < Median < Mean   Mode > Median > Mean
–Stem-leaf
–Boxplot
–Skewness
Displaying and Exploring Data

Review

Chapter 3:
Dispersion
–Range
–Variance (SD2)
–Standard Deviation
 (SD)
–Coefficient of
 variation (CV)


Chapter 4:
Displaying and
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness
Displaying and Exploring Data

Review

Chapter 3:
Dispersion
–Range
–Variance (SD2)
–Standard Deviation
 (SD)
–Coefficient of
 variation (CV)


Chapter 4:
Displaying and
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness




                             minimum   Q1   Median   Q3   maximum
Review

Chapter 3:
Dispersion
–Range
–Variance (SD2)
–Standard Deviation
 (SD)
–Coefficient of
 variation (CV)


Chapter 4:
Displaying and
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness             •The graph is called a cumulative frequency distribution.

                      •The interquartile range is 45-35=10 years and the median is 40 years
                       a. 10   b.35   c.40    d.45   e.15   f.20
                      •50% of the employees are between 35 years and 45 years old.
What we have learnt?
1. Why Failed in
Statistics?
                   • Review

2. Chapter 1:
What is            • Chapter 3: Dispersion
Statistics?
A.Why? What?          •   Range
B.Types of
 statistics,          •   Variance (SD2)
 variables
C.Levels of           •   Standard Deviation (SD)
 measurement
                      •   Coefficient of variation (CV)

3. Chapter 2:
Describing Data    • Chapter 4: Displaying and exploring data
A.Frequency
 tables
                      •   Dotplot
B.Frequency           •   Stem-leaf
 distributions
C.Graphic             •   Boxplot
 presentation
                      •   Skewness

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Lesson 3

  • 1. Hanze University of Applied Science Groningen Ning Ding, PhD Lecturer of International Business School (IBS) n.ding@pl.hanze.nl
  • 2. What we are going to learn? • Review • Chapter 3: Dispersion • Range • Variance (SD2) • Standard Deviation (SD) • Coefficient of variation (CV) • Chapter 4: Displaying and exploring data • Dotplot • Stem-leaf • Boxplot • Skewness
  • 3. Review a b Review Chapter 3: Discrete counting Continuous measuring Dispersion –Range –Variance (SD2) –Standard Deviation (SD) –Coefficient of variation (CV) Chapter 4: Displaying and 1.Age 5. Salary exploring data –Dotplot –Stem-leaf 2.Sales volume 6. Class size –Boxplot –Skewness 3. Temperature 7. Height 4. Weight 8. Shoe size (NL)
  • 4. Review Constructing Frequency Distribution: Quantitative Data a. 4 b.5 c.6 d.70 25 = 32, 26 = 64, suggests 6 classes Use interval of 100 a. 80 b.100 c.120 d.150 i> 571- 41 = 88.33 6 P46. N.30 Ch.2
  • 5. Review 0 Cumulative Class interval = 100 relative relative P46. N.30 Ch.2
  • 6. Central Tendency : Mean, Mode, Median Mean: Average SCCoast, an Internet provider in the Southeast, developed the following frequency distribution on the age of Internet users. Describe the central tendency: X = 2410 / 60 = 40.17 (years) P87 N.60 Ch.3
  • 7. Review Central Tendency : Mean, Mode, Median Mean: Average Mode: Most Frequency SCCoast, an Internet provider in the Southeast, developed the following frequency distribution on the age of Internet users. Describe the central tendency: Mode = 45 (years) P87 N.60 Ch.3
  • 8. Review Central Tendency : Mean, Mode, Median Mean: Average Mode: Most Frequency Median: Midpoint SCCoast, an Internet provider in the Southeast, developed the following frequency distribution on the age of Internet users. Describe the central tendency: a.40.25 b.41.25 c.30.50 d.37.50 Median = ? (years) P87 N.60 Ch.3
  • 9. Review Step 1: Define the location of the median Step 2: Calculate the median M Lm=(60+1)/2=30.5 Value:40 50 Location: 28 48 30.5 30.5-28 M-40 = 48-28 50-40 Median= 41.25 P87 N.60 Ch.3
  • 10. Dispersion Review Range Chapter 3: Dispersion –Range –Variance (SD2) –Standard Deviation (SD) Variance (SD2) and Standard Deviation (SD) –Coefficient of variation (CV) Chapter 4: Displaying and Interquartile Range exploring data –Dotplot –Stem-leaf –Boxplot Coefficient of variation (CV) –Skewness
  • 11. Dispersion Review – tells us about the spread of the data. Chapter 3: – Help us to compare the spread in two or more Dispersion distributions. –Range –Variance (SD2) –Standard Deviation (SD) –Coefficient of variation (CV) Chapter 4: Displaying and exploring data –Dotplot –Stem-leaf –Boxplot –Skewness
  • 12. Dispersion: Range Review Range: Chapter 3: is the difference between the largest and Dispersion –Range the smallest value in a data set. –Variance (SD2) –Standard Deviation (SD) –Coefficient of variation (CV) Example: Chapter 4: Displaying and To find the range in 3,5,7,3,11 exploring data –Dotplot –Stem-leaf Range = 11-3 = 8 –Boxplot –Skewness
  • 13. Dispersion: Variance Review Population Variance: • is the mean of the squared difference between each Chapter 3: Dispersion value and the mean. –Range • overcomes the weakness of the range by using all the –Variance (SD2) –Standard Deviation values in the population. (SD) –Coefficient of variation (CV) Σ(X - μ) 2 σ2 = Chapter 4: N Displaying and exploring data –Dotplot –Stem-leaf Sample Variance: –Boxplot Σ(X - X) 2 –Skewness s2 = n -1
  • 14. EXAMPLE – Variance Variance Dispersion: and Standard Deviation Population Variance: Σ(X - μ) 2 σ2 = Review N The number of traffic citations issued during the last five months in Chapter 3: Dispersion Beaufort County, South Carolina, is 38, 26, 13, 41, and 22. What –Range is the population variance? –Variance (SD2) –Standard Deviation Step 2: Find the difference between each observation and the mean (SD) –Coefficient of variation (CV) Chapter 4: Displaying and Step 1: Get the mean exploring data –Dotplot –Stem-leaf –Boxplot –Skewness Step 3: Square the difference and sum up Step 4: Divided by N 27
  • 15. Dispersion: Standard Deviation Review Chapter 3: Dispersion Population Standard Deviation: –Range –Variance (SD2) is the square root of the population variance. –Standard Deviation σ= σ2 (SD) –Coefficient of variation (CV) Chapter 4: Displaying and exploring data –Dotplot Sample Standard Deviation: –Stem-leaf –Boxplot is the square root of the sample variance. –Skewness s = s2
  • 16. Dispersion: Standard Deviation Example: Review The hourly wages earned by a sample of five students are: €7, €5, €11, €8, €6. Chapter 3: Dispersion Find the variance and standard deviation. –Range Step 1: Get the mean ΣX 37 –Variance (SD2) X= = = 7.40 –Standard Deviation (SD) n 5 2 Σ(X - X ) 2 2 –Coefficient of Step 2: Sum up the (7 - 7.4) + ... + (6 - 7.4) variation (CV) squared differences s2 = = n -1 5 -1 Chapter 4: 21.2 Displaying and = = 5.30 exploring data –Dotplot Step 3: Divided by N-1 5 -1 –Stem-leaf –Boxplot –Skewness Step 4: Square root it s = €2.30 The variance is €5.30; the standard deviation is €2.30.
  • 17. Dispersion: Standard Deviation Review Chapter 3: Dispersion Compare –Range –Variance (SD2) –Standard Deviation (SD) –Coefficient of 20 40 50 60 80 20 49 50 51 80 variation (CV) Chapter 4: Displaying and Step 1: Get the mean exploring data –Dotplot –Stem-leaf Step 2: Sum up the –Boxplot squared differences –Skewness Step 3: Divided by N-1 Step 4: Square root it
  • 18. Dispersion: Standard Deviation Review Chapter 3: Dispersion Compare –Range –Variance (SD2) –Standard Deviation (SD) –Coefficient of 20 40 50 60 80 20 49 50 51 80 variation (CV) Chapter 4: Displaying and exploring data •The sales of –Dotplot –Stem-leaf MANGO is more –Boxplot –Skewness closely clustered around the mean of 50 than the sales of ZARA.
  • 19. Dispersion: Standard Deviation Review Chapter 3: Dispersion –Range –Variance (SD2) –Standard Deviation (SD) –Coefficient of variation (CV) Chapter 4: Displaying and exploring data –Dotplot –Stem-leaf –Boxplot –Skewness The standard deviation decreases because the new value 20 is very close to the mean 20.36.
  • 20. Dispersion: Standard Deviation Step 1: Step 3: Use f * (Mid-Mean)2 Find the Midpoint Step 2: Calculate the Mean P87 N.60 Ch.3
  • 21. Dispersion: Standard Deviation Step 4: Calculate the Variance Step 5: Calculate the Standard Deviation P87 N.60 Ch.3
  • 22. Dispersion: Coefficient of Variation Review Coefficient of Variation: Chapter 3: describes the magnitude sample values and the variation within Dispersion them. –Range –Variance (SD2) –Standard Deviation (SD) –Coefficient of variation (CV) The following times were recorded by the quarter-mile and mile runners of a Chapter 4: university track team (times are in minutes). Displaying and exploring data Quarter-Mile Times: 0.92 0.98 1.04 0.90 0.99 –Dotplot –Stem-leaf Mile Times: 4.52 4.35 4.60 4.70 4.50 –Boxplot After viewing this sample of running times, one of the coaches commented that –Skewness the quarter milers turned in the more consistent times. Calculate the appropriate measure to check this and comment on the coach’s statement. We can compare the dispersion with the coefficient of variation because they have different “magnitudes”.
  • 23. Dispersion: Coefficient of Variation Quarter-Mile Times: 0.92 0.98 1.04 0.90 0.99 Mile Times: 4.52 4.35 4.60 4.70 4.50
  • 24. Dispersion: Coefficient of Variation The following times were recorded by the quarter-mile and mile runners of a Review university track team (times are in minutes). Chapter 3: Quarter-Mile Times: 0.92 0.98 1.04 0.90 0.99 Dispersion Mile Times: 4.52 4.35 4.60 4.70 4.50 –Range –Variance (SD2) After viewing this sample of running times, one of the coaches commented that –Standard Deviation the quarter milers turned in the more consistent times. Calculate the appropriate (SD) measure to check this and comment on the coach’s statement. –Coefficient of variation (CV) We can compare the dispersion with the coefficient of variation because they have different “magnitudes”. Chapter 4: Displaying and exploring data –Dotplot –Stem-leaf –Boxplot –Skewness No, the mile-time team showed more consistent times.
  • 25. Displaying and Exploring Data Review Dot plots: Chapter 3: Dispersion –Range –Variance (SD2) –Standard Deviation (SD) –Coefficient of variation (CV) Chapter 4: Displaying and exploring data –Dotplot –Stem-leaf –Boxplot –Skewness
  • 26. Displaying and Exploring Data Review Stem-and-Leaf Displays: Chapter 3: Each numerical value is divided into two parts. The leading Dispersion –Range digit(s) becomes the stem and the trailing digit the leaf. The –Variance (SD2) stems are located along the vertical axis, and the leaf values are –Standard Deviation (SD) stacked against each other along the horizontal axis. –Coefficient of variation (CV) Chapter 4: Displaying and exploring data –Dotplot –Stem-leaf –Boxplot –Skewness Stem
  • 27. Displaying and Exploring Data Stem-and-Leaf Displays: Review Chapter 3: Dispersion –Range –Variance (SD2) –Standard Deviation (SD) –Coefficient of variation (CV) Chapter 4: Displaying and exploring data –Dotplot –Stem-leaf –Boxplot –Skewness
  • 28. Displaying and Exploring Data Review Quartiles, Deciles, and Percentiles Chapter 3: Alternative ways of describing spread of data include determining Dispersion the location of values that divide a set of observations into equal –Range parts. –Variance (SD2) –Standard Deviation (SD) –Coefficient of variation (CV) Chapter 4: Displaying and exploring data –Dotplot –Stem-leaf –Boxplot –Skewness
  • 29. Displaying and Exploring Data Review Quartiles, Deciles, and Percentiles Chapter 3: Dispersion –Range –Variance (SD2) –Standard Deviation (SD) –Coefficient of variation (CV) Chapter 4: Displaying and exploring data –Dotplot –Stem-leaf –Boxplot –Skewness
  • 30. Displaying and Exploring Data Review Quartiles, Deciles, and Percentiles Chapter 3: Dispersion Raw Percentile –Range Score Frequency Frequency Rank –Variance (SD2) –Standard Deviation (SD) 95 1 25 100 –Coefficient of 93 1 24 96 variation (CV) 88 2 23 92 Chapter 4: 85 3 21 84 Displaying and exploring data 79 1 18 72 –Dotplot 75 4 17 68 –Stem-leaf –Boxplot 70 6 13 52 –Skewness 65 2 7 28 62 1 5 20 58 1 4 16 54 2 3 12 50 1 1 4 N = 25
  • 31. Displaying and Exploring Data Review Quartiles, Deciles, and Percentiles Chapter 3: Dispersion –Range –Variance (SD2) –Standard Deviation (SD) –Coefficient of variation (CV) Example: Chapter 4: Displaying and 101 43 75 61 91 104 exploring data –Dotplot –Stem-leaf –Boxplot –Skewness The first quartile is ?
  • 32. Displaying and Exploring Data Review Chapter 3: Step 1: Organize the data from lowest to largest value Dispersion –Range 101 43 75 61 91 104 –Variance (SD2) –Standard Deviation P1 P2 P3 P4 P5 P6 (SD) –Coefficient of variation (CV) Step 2: P1.75 Chapter 4: Displaying and exploring data Step 3: Draw two lines –Dotplot –Stem-leaf –Boxplot –Skewness 43 61-43 = 18 61 P1 0.75 P2
  • 33. Displaying and Exploring Data Review Chapter 3: Dispersion –Range –Variance (SD2) –Standard Deviation Step 3: Draw two lines (SD) –Coefficient of variation (CV) 43+13.5 = 56.5 Chapter 4: Displaying and 43 61-43 = 18 61 exploring data –Dotplot –Stem-leaf –Boxplot P1 0.75 * 18 = 13.5 P2 –Skewness The first quartile is 56.5.
  • 34. Displaying and Exploring Data Listed below, ordered from smallest to largest, are the number of visits last week. a. Determine the median number of calls. a. 57median is 58. The b.58 c.59 d.56 b. Determine the first and third quartiles. Q1 = 51.25 Q3 = 66.00 a. 50.25 b.51.25 c.60.00 d.62.25 e.63.00 f. 66.00 P110. N.14 Ch.4
  • 35. Displaying and Exploring Data Listed below, ordered from smallest to largest, are the number of visits last week. c. Determine the first decile and the ninth decile. D1 = 45.30 D9 = 76.40 d. Determine the 33rd percentile. P33 = 53.53 P110. N.14 Ch.4
  • 36. Displaying and Exploring Data Review Box Plots A graphical display, based on quartiles to visualize a set of data. Chapter 3: Dispersion –Range minimum Q1 Median Q3 maximum –Variance (SD2) –Standard Deviation (SD) –Coefficient of variation (CV) Chapter 4: Displaying and exploring data –Dotplot –Stem-leaf –Boxplot –Skewness
  • 37. Displaying and Exploring Data Review Box Plots A graphical display, based on quartiles to visualize a set of data. Chapter 3: Dispersion –Range –Variance (SD2) –Standard Deviation minimum Q1 Median Q3 maximum (SD) –Coefficient of variation (CV) Chapter 4: Displaying and exploring data –Dotplot –Stem-leaf –Boxplot –Skewness
  • 38. Displaying and Exploring Data Review Chapter 3: Dispersion –Range –Variance (SD2) –Standard Deviation (SD) –Coefficient of variation (CV) Chapter 4: Displaying and Zero skewness positive skewness negative skewness exploring data –Dotplot mode=median=mean Mode < Median < Mean Mode > Median > Mean –Stem-leaf –Boxplot –Skewness
  • 39. Displaying and Exploring Data Review Chapter 3: Dispersion –Range –Variance (SD2) –Standard Deviation (SD) –Coefficient of variation (CV) Chapter 4: Displaying and exploring data –Dotplot –Stem-leaf –Boxplot –Skewness
  • 40. Displaying and Exploring Data Review Chapter 3: Dispersion –Range –Variance (SD2) –Standard Deviation (SD) –Coefficient of variation (CV) Chapter 4: Displaying and exploring data –Dotplot –Stem-leaf –Boxplot –Skewness minimum Q1 Median Q3 maximum
  • 41. Review Chapter 3: Dispersion –Range –Variance (SD2) –Standard Deviation (SD) –Coefficient of variation (CV) Chapter 4: Displaying and exploring data –Dotplot –Stem-leaf –Boxplot –Skewness •The graph is called a cumulative frequency distribution. •The interquartile range is 45-35=10 years and the median is 40 years a. 10 b.35 c.40 d.45 e.15 f.20 •50% of the employees are between 35 years and 45 years old.
  • 42. What we have learnt? 1. Why Failed in Statistics? • Review 2. Chapter 1: What is • Chapter 3: Dispersion Statistics? A.Why? What? • Range B.Types of statistics, • Variance (SD2) variables C.Levels of • Standard Deviation (SD) measurement • Coefficient of variation (CV) 3. Chapter 2: Describing Data • Chapter 4: Displaying and exploring data A.Frequency tables • Dotplot B.Frequency • Stem-leaf distributions C.Graphic • Boxplot presentation • Skewness