# Measures of Variability

Measuresof Variability

 Number of arrests Bob 0 Barbara 0 Johny 1 Sam 1 Ken 2 Nicole 2 Sarah 3 Stuart 3 Julie 5 Keith 8
1. Range of the sample

Rangeis usually calculated by getting the difference between the highestand the lowest value.

Range=maximumvalue-minimum value

=8-0

=8

1. Interquartile Range

Theinterquartile range is a measure of variability that largely concernsitself with the division of data sets in quartiles. Quartiles dividea data set that is ordered in four equal sections. The values thatare obtained and divide each section is known as first, second andthird quartiles.

Interquartilerange =3rdquartile – 1stquartile

Positionfor 1stquartile ===2.75≈ 3

The1stquartile=1

Positionfor 3rdquartile ===8.25≈ 9

The3rdquartile=3

Interquartilerange =3-1=2

1. Variance of the sample

=

Samplemean=== 2.5

=

=

==6.0556

Samplevariance is 6.0556.

1. Standard deviation of the sample

Samplestandard deviation=

=2.46

Fromthe above calculations, the difference between the maximum arrestsand the minimum arrests is 8. The interquartile range is the rangethat contains 50% of the number of arrests in this sample (Pinedaet al., 2013). From the calculations and in this case among the middle 50% of theoffences committed the difference between the highest arrests that isthe 3rdquartile and the least arrests that is the 1stquartile is 2 arrests.

Thenumber of arrests in this sample on average deviate away from theaverage number of arrests of the inmates by 2.46. The variance is theaverage squared differences from the mean of the number of arrests ofthe inmates.

References

Pineda,M., Aguilar, A., Axotla, J. C., León, F., &amp García, O. (2013).TEACHING THE TOPIC OF CENTRAL MEASURES TENDENCY AND VARIABILITYTHROUGH OF E-LEARNING COURSE, IN THE CLASS OF STATISTIC IN THE HIGHERFACULTY OF STUDIES CUAUTITLAN. EDULEARN13Proceedings,4554-4558.