Question

Subject Number of years in prison before release
1    16
2 9
3    17
4    30
5    20
6    18

a) For the above data, calculate and interpret all appropriate measures of central
tendency.
b) Calculate and interpret the range, variance, and the standard deviation.
c) Say we added a subject who spent 60 years in prison before exoneration. In statistics,
what would we call this individual?

Answer 1

a) The measures of central tendency are

(i) Mean

(ii) Median,

Observations in ascending order are 9,16,17,18,20,30

Median means middle value of sorted values. Since there are 6 values, median will be the average of the 3rd and 4th values

Median =(17+18)/2 = 17.5

(iii) Mode

Mode means most repeating term. Since all values appear exactly once, there is no mode for this data set.

b) Range= Highest value- Lowest value

Range =30-9 =21

c) Variance,

We know,

N=6

Standard deviation,

c) This individual is called an outlier. An outlier is an observation point that is distant from other observations.