Question

design your own measure of variability that minimizes the effect of extreme scores and is measured in thesame units as the original data. Dwmonstrate that your measure meets the requirements, and contrast it to other measures of variability

Answer 1

The different measures of variability are:
1) variance: is the average squared deviation from the population mean and is mathematically given by where x_i is each value

The unit of variance is not measured in the same units as that of the original data.

2) Range: difference between the largest and smallest value. It is completely based on the extreme values.

3) Quartile Deviation: is given by the difference of third and first quartile divided by 2.

Both range and quartile deviation depend on extreme values.

Purposed measure:

Standard deviation which is the square root of variance. It minimizes the effect of extreme values and has the same unit as that of the data.

Example: Suppose diameter of 6 balls in millimeters is 4,8,8,8,9,9. then

the range is 9-4 = 5 millimeters

the quartile deviation is millimeters

The variance is 2.888 millimeter square.

and the standard deviation is 1.6997 millimeters

Thus standard deviation is the best method to compute variability as it is least affected by extreme observations and has the same unit as that of the original data