Variance

Square of the standard deviation is termed as variance.

The semi inter-quartile range

- It is a measure of dispersion which includes the use of quartile. A quartile is a mark or a value that lies at the boundary of a division when any type of given set of data is divided into four equal divisions

- All of such divisions normally carry 25 percent of all the observations

- The semi inter-quartile range is a good measure of dispersion since it shows how the rest of the data are normally spread around the mean

- The quartiles generally used are three namely;

i. The lower quartile as first quartile Q1 this usually binds the lower 25 percent of the data

ii. The median as second quartile Q2

i. The upper quartile (third quartile Q3)

The semi-inter-quartile range,

SIR = (Q3 - Q1)/2       

Illustration 1

The weights of 15 parcels recorded at the GPO were given as:

16.2, 17, 20, 25(Q1) 29, 32.2, 35.8, 36.8(Q2) 40, 41, 42, 44(Q3) 49, 52, 55 (in kgs)

Required

Find out the semi-inter-quartile range for the above data

SIR = (Q3 - Q1)/2

= (44 - 25)/2

= 19/2

 = 8.5