The most frequently used measures of central tendency for quantitative data are the mean and the median. Accordingly, the most frequent measures of variability are standard deviation and interquartile range (IQR).
You calculate the mean and standard deviation while the median and IQR are positions in the data.
Table 1
Central Tendency and Variability Choices
Table has three columns: Data Measure, Normal Data, Extreme Skewed Data. It shows the measure associated with central tendency and variability for each condition, Normal or Skewed.
The attached Week 2 Discussion Data file shows a sample of Civil Service examination scores from 30 applicants to law enforcement jobs. Do these steps.
Steps
A. Use Excel to calculate descriiptive statistics. Included are the means, sample standard deviation, IQR, and the five-number summary. The five-number summary includes Min, Quartile 1, Median, Quartile 3, and Max. Examples of the calculations are in the Data file.
B. Construct a Single Box and Whisker Plot
1. Use the column Scores and select all data in that column
2. Use Insert > Insert Statistic Chart > Box and Whisker
3. Finish the chart with a y-axis label.
This chart depicts the five-number summary. (Refer to LO 4-8).
C. Examine the box and whisker plot. Does it indicate outliers? If so, which one(s)? Are any considered extreme outliers? Refer to the calculation example in the Data File.
D. Would you choose to use the mean or the median as the dataset’s central tendency measure? What makes that determination? Explain. (Refer to Table 1 and Doane et al. LO 4-2).
E. What are your thoughts about people who use the means to describe data that is extremely skewed? Would that be deceptive and ethically incorrect?
Week 2 Discussion Data Civil Service Examination Scores
Exam Scores Use the sample standard deviation.
60
62
63
63
64
66
67
69
69
70
71
71
73
74
75
75
77
78
80
83
85
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90
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97
Excel Calculation Example
Example Statistic
Calculation
Excel Functions
18 Mean, x̅ 76.5 =AVERAGE(B4:B27)
50 SD, s 18.6 =STDEV.S(B4:B27) Sample Standard Deviation
57 Min 18 =MIN(B4:B27)
62 Q1 67.8 =QUARTILE(B4:B27,1)
64 Median 81 =MEDIAN(B4:B27)
67 Q3 87.0 =QUARTILE(B4:B27,3)
68 Max 107 =MAX(B4:B27)
68 IQR 19.3 =Q3-Q1 Calculation
73 Count 24 =COUNT(B4:B27)
74
78
80
82
82
82
83
83
85
93 Max Q3 IQR Outlier Extreme
93 107 87.0 19.3 116 144.75 No outliers.
93
96 Min Q1 IQR Outlier Extreme
98 18 67.8 19.3 39 10 Min is betwee Outlier and Extreme
107
The Min would need to be less than 10 to be an extreme outlier
The Min = 18 is between 10 and 39, thus non-extreme outlier
Reference
Doane, D., Seward, L. (2019) Applied statistics in business and economics (6th ed). McGraw-Hill
Web Calculators
Statistics Kingdom. (2021). Box plot maker. https://www.statskingdom.com/boxplot-maker.html
