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Quantitative Reasoning - Central Tendency and Dispersion measures

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You have administered a standardized test of manual dexterity to two groups of 10 semi skilled workers. One of these two groups of workers will be employed by you to work in a warehouse with many fragile items. The higher the manual dexterity of a worker the less likelihood that worker will break significant inventory. Because of a unique contract you must hire all 10 employees from one of the two groups and none of the employees from the other.

Group A Scores Group B Scores
77 100
87 99
80 62
91 57
77 95
84 96
90 69
60 32
79 83
66 98

You must decide which group to choose. Consider at least two measures of central tendency and at least one measure of dispersion for each group and use those to make your choice. Be sure to justify your choice with at least one page of discussion and analysis. Can you base a decision on the information provided and the measures that you calculated only?

Calculate and report the mean, median, and mode of the data (at lease 20 observations, preferably more).
(any observations) i will use telephone calls in 20 days
day 1 (4) day 2 (20) day 3 (6) day 4 (8) day 5 (9)
day 6 (15) day 7 (11) day 8 (1) day 9 (22) day 10 (4)
day 11 (8) day 12 (7) day 13 (7) day 14 (3) day 15 (4) day 16 (3) day 17 (6) day 18 (5) day 19 (8) day 20 (13)

Now calculate the standard deviation of the data. For this calculation compute the difference between each one of the observations and the mean, (this number may be positive or negative), then multiply each of these differences by itself, then add all of these products, and finally divide the sum total by the number of observations. You'll get the "VARIANCE". Now take the square root of this number and you get what is called the "STANDARD DEVIATION" that measures the dispersion of the data from their mean.

Refer first to the measures of central tendency - the mean, the median and the mode. Are these numbers higher or lower that you would have expected? Which of these measures of central tendency do you think most accurately describes the lifestyle variable you are looking at?

Are you surprised by the number you have obtained for the standard deviation?
Write a brief paper with your calculations and the answers to these questions.

Solution

For the first part, mean and median are computed as central tendency measures and Standard deviation is computed as the measure of dispersion. In the second part, all the calculations are completed and a discussion is also included in the solution based on the results. The attached zip file has a word document with the answers and an excel sheet with the calculations.

No. of Words: 828 words Help

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Price: $6.00

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Quantitative Reasoning - Central Tendency and Dispersion measures

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