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Descriptive Statistics for Analyzing Quantitative Data
You are in charge of the HR Department for your agency and one of your primary responsibilities is to recruit and interview applicants. You heard from a colleague in a comparable position at another agency that they use an instrument that has been very helpful with this task called the UPickdM Test. You decide to try the Test and administer it to the next 10 applicants you see. The Test assigns scores based on ratings of performance on several role-playing exercises by a highly qualified judge with several years of experience. Your applicants all take the Test, and their scores are shown below. Since this is your first experience with the UPickdM Test you do not know if these scores are relatively high or low, so you ask your colleague in the comparable agency if you could have the scores on the same test of ten individuals who are model employees. That way, you could see if your applicants compare with the high scoring ones in the other agency and make your hiring choices based on these results.
UPickdM Test Scores for:
Your Applicants Other Agencyâs Employees
61 78
51 83
73 81
42 66
91 81
80 89
77 85
73 79
64 71
88 77Calculate the measures of central tendency for the two groups.
Which measure of central tendency do you think is the best one to use to give a picture of the average participant in each group? (your response does not have to be the same for both groups)
Calculate the measures of variability for the two groups.
Which measure of variability do you think is the best one to use to give a picture of the average participant in each group? (your response does not have to be the same for both groups)
Now compare the mean and variance for both groups. What does this tell you?
Sample Answer
Calculate the measures of central tendency for the two groups.
Your Applicants:
- Mean: (61 + 51 + 73 + 42 + 91 + 80 + 77 + 73 + 64 + 88) / 10 = 700 / 10 = 70
- Median: First, order the scores: 42, 51, 61, 64, 73, 73, 77, 80, 88, 91. The median is the average of the two middle scores: (73 + 73) / 2 = 73
- Mode: The score that appears most frequently is 73 (appears twice).
Other Agency’s Employees:
- Mean: (78 + 83 + 81 + 66 + 81 + 89 + 85 + 79 + 71 + 77) / 10 = 790 / 10 = 79
- Median: First, order the scores: 66, 71, 77, 78, 79, 81, 81, 83, 85, 89. The median is the average of the two middle scores: (79 + 81) / 2 = 80
- Mode: The score that appears most frequently is 81 (appears twice).
2. Which measure of central tendency do you think is the best one to use to give a picture of the average participant in each group? (your response does not have to be the same for both groups)
-
Your Applicants: The median (73) might be the best measure of central tendency for your applicants. The mean (70) is slightly pulled down by the lower scores (42 and 51), which might not be truly representative of the “typical” applicant. The median is less sensitive to extreme values.
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Other Agency’s Employees: The mean (79) and the median (80) are quite close for the other agency’s employees. In this case, the mean (79) could be considered a good representation of the average model employee’s score, as the scores are relatively clustered without extreme outliers significantly skewing the average.
3. Calculate the measures of variability for the two groups.
Your Applicants:
- Range: Highest score (91) – Lowest score (42) = 49
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