2. In general, an interval variable is described using 1) measures of central te
ID: 3067384 • Letter: 2
Question
2. In general, an interval variable is described using 1) measures of central tendency; and 2) measures of dispersion. The variable of interest is sentence length. See the data below. These data represent sentences for 12 cases (6 each for Judges A and B) Judge A 34 months 30 months 31 months 33 months 36 month:s 34 months Judge B 26 months 43 months 22 months 35 months 20 month:s 34 month:s Case 1 Case 2 Case 3 Case 5 Case 6 Mean Standard 33 months 2 months 30 months 8.1 months Deviatiorn a. Explain the difference between a Measure of Central Tendency and a Measure of b. Which judge (Judge A or Judge B) is harsher in his/her sentencing? How do you c. Which judge (Judge A or Judge B) appears to use more discretion (more varied Dispersion (or Variability) know? Which statistic did you use to draw the conclusion? sentences) in his/her sentencing? Which statistic did you use to draw the conclusion?Explanation / Answer
a. Difference between Measure of Central Tendency and Measure of Dispersion
b. Calculating the median of the Judge-A
Listing the sentence length in the ascending order.
30, 31, 33, 34, 34, 36
Since, even number of observations, taking the Average of two middle numbers:
=(33+34)/2 = 33.5
Calculating the median of the Judge-B
Listing the sentence length in the ascending order.
20, 22, 26, 34, 35, 43
Since, even number of observations, taking the Average of two middle numbers:
=(26+34)/2 = 30
Since the median sentence length by Judge-A (i.e. 33.5) is greater than that of Judge-B (i.e. 30), Judge-A is harsher than Judge-B.
c. Variance statistic gives the insight into the discretion of each judge because this statistic measures how far or near a data distribution is spread out from its mean.
Variance is given by: ((Summation of squared observation)/(Total # of observations)) - (Mean squared)
Variance of Judge-A = 4
Variance of Judge-B = 65
Since the variance of Judge-B is much much higher than that of Judge-A, we can conclude that Judge-B is using more discretion (or more varied) than Judge-A.
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