2. In general, an interval variable is described using 1) measures of central te

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.   Measure of central tendency will give us information about the middle value or central value of the variable around which whole of our data set is spread. Whereas, the measure of dispersion will give us information that on average, how much variability is existing in the data as we move from one observation to another observation.

b. Judge A is harsher in his sentencing because mean value of the length of sentences given by him is 33 months which is greater than the mean value of the length of sentences given by judge B which is 30 months. We used the MEAN as a statistic for this conclusion.

c. Judge B appears to use more discretion in his sentencing because standard deviation of the length of sentences given by him is 8.1 months which is greater than the std. deviation of the length of sentences given by judge A which is 2 months. We used the STANDARD DEVIATION as a statistic for this conclusion.

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