1wsSMAM 319 Some Examples of Graphical Display of Data

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1 1wsSMAM 319 Some Examples of Graphical Display of Data 1. Lands End employs numerous persons to take phone orders. Computers on which orders are entered also automatically collect data on phone activity. One variable useful in predicting staffing levels is the number of calls per shift handled by each employee. From the data collected on 25 workers, calls per shift are given in the Minitab output below. Worksheet size: 1 cells MTB > set c1 DATA> DATA> end MTB > stem and leaf c1 Stem-and-leaf of C1 N = 25 Leaf Unit = (6) MTB > histogram c1 Mail Order Firm C Average: Std Dev: N of data: 25 C Anderson-Darling Normality Test A-Squared:.314 p-value:.523 MTB > %NormPlot c1; SUBC> Title 'Mail Order Firm'. Executing from file: NormPlot.MAC Macro is running... please wait MTB > MTB > dotplot c1

2 Character Dotplot.....:.. :..:... : C Descriptive Statistics Variable N Mean Median TrMean StDev SEMean C Variable Min Max Q1 Q3 C MTB > boxplot c Another Example Physical education researchers interested in the development of the over arm throw, measured the horizontal velocity of a thrown ball at the time of release. The results for first grade children ( in feet/sec) are given below.\

3 MTB > print c2 c3 Data Display Row males females MTB > name c2='males' MTB > name c3='females' MTB > stem andleaf c2 Stem-and-leaf of males N = Leaf Unit = (7) MTB > stem and leaf c3 Stem-and-leaf of females N = 17 Leaf Unit = (5)

4 males females MTB > histogram c2 c3 MTB > boxplot c2 c3 MTB > dotplot c2 c3 Character Dotplot... :... : ::..: males :..... : females MTB > describe c2 c3 Descriptive Statistics Variable N Mean Median TrMean StDev SEMean males females Variable Min Max Q1 Q3 males females

5 An example of simulated data that is not normally distributed. Thisdata is a simulation of data from the continuous uniform distribution 1 < X < f(x) = MTB > random 1 c3; SUBC> uniform. MTB > stem and leaf c3 Stem-and-leaf of C3 N = 1 Leaf Unit = (1) MTB > describe c3 Descriptive Statistics Variable N Mean Median TrMean StDev SEMean C Variable Min Max Q1 Q3 C MTB > nscores c3 c4 MTB > boxplot c3 MTB > plot c4*c3 MTB > C3 Boxplot Normal Plot

6 Note that although the distribution is symmetric there is considerable departure from normality. The following scores represent the final examination grade for an elementary statistics course ` Using Minitab make A. a stem and leaf display; B. a boxplot.; C. a frequency histogram; D. a dotplot; E. a five number summary using the Describe command. Answer the following questions A. Does the data appear to be normally distributed? Is it skewed in any particular direction? Are there any outliers? Are they curve breakers or people who probably have not been studying? Is the mean and the median much different. If so what might that mean? B. Assign letter grades A-F on the curve based on: (1) the places where there are breaks in the distribution; (2) ranking the grades and giving 1% A % B % C % D and 1% F ; (3) making intervals using the estimates of the mean and the standard deviation to compute the students Z scores using the percentiles of the normal distribution. C. How do you account for whatever differences in the grade distribution that exist using each of the three methods above? Which method of grading on the curve if any do you think is most sensible? MTB > stem and leaf c5 Stem-and-leaf of C5 N = Leaf Unit = (6)

7 MTB > boxplot c5 MTB > histogram c5 MTB > dotplot c5 Character Dotplot...:.: : :.. ::. :::.:.:.:.::::.:.: C MTB > describe c5 Descriptive Statistics Variable N Mean Median TrMean StDev SEMean C Variable Min Max Q1 Q3 C MTB > %NormPlot c5; SUBC> Title 'Normal Plot for Grade Distribution'. Executing from file: NormPlot.MAC Macro is running... please wait MTB > let c6=65.48 MTB > let c7 =21.13 MTB > let c8=(c5-c6)/c7 MTB > sort c8 c9 MTB > print c9 Data Display C MTB > sort c5 c1 MTB > print c1 Data Display C

8 MTB > C5 Normal Plot for Grade Distribution C5 Average: Std Dev: N of data: Anderson-Darling Normality Test A-Squared: 1.5 p-value:.

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