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 is that figure which is representatiive of an entire dataset.It can be understood as the figure about which the data point lie. For example the data set {1,2,4,6,7} can be said to lie about 4. The central tendency is measured by the mean , median or mode.

Wheras the Dispersion of the data is the figure which tells how much concentrated or how much spread the data points are with respect to a point(usually some central measure). For example we can see that a data set as{1,2,3} is less scattered as the data set{1,3,5}. Some measures of the dispersion are Range, Varaince, Mean Deviation about mean(or any other point) etc.

b) Judge A is harsher. To see which judge is harsher we check whose average is more.

Average sentence length by Judge A(33 months) is greater than that by judge B(30 months).

We have used the Mean to draw this conclusion.

c) Judge B is more discrete (more varied) because standard deviation of sentencing by Judge B (8.1 months) is more than that by Judge A (2 months). We have used the standard deviations to come to this conclusion.

Thank you.

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