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) The difference between measures of central tendency and measures of dispersion is that central tendency, convert the entire data into a single numerical value and where as dispersion means that how the variable varies (scattered) from one plce to another place from the mean.

The best measure in central tendency is the mean and in dispersion is the standard deviation.

b) Judge 'A'.

The mean number of Judge 'A' was found to be more than the mean number of Judge'B'

Sample mean is used to draw the conclusion

c) Judge 'B' appers to use more discretion (8.1 months > 2 months)

Standard deviation is used to draw the conclusion

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