What are the Measures of Variation in Data Collection?

Two sets of data may have the same central location and yet, be quite different from each other. It is possible if one of these is more spread out than the other one.

The mean of all the three curves is the same but Curve X has less spread (or variation) than Curve Y. Further, Curve Y has less variation than Curve Z. If we measure only the mean of these three distributions, then we would miss an important difference between the three curves. The variable in the data can be studied with the help of measures of variation. The major objectives of measuring variation or dispersion are as follows:

(i) To determine the liability of an average value.

(ii) To compare two or more series with regard to their variability.

(iii) To serve as a basis for the control of variability.

(iv) To facilitate the use of other statistical measures.

Variations or dispersion are measured by four means-range, quartile deviation, mean deviation and standard deviation.

Range

Range is defined as the difference between the highest value and the lowest value of avariabkijjal series. The relative measure of range is known as Co-efficient of Range and is calculated as follows:

Co – efficient of Range = Largest Item – Smallest Item

Largest Item + Smallest Item Example: Find out the range and co-efficient of range of the following distribution:

Hourly Wages (In Rs)

Here, the maximum wage is Rs 15 and the minimum wage is Rs 6 Range = largest Item – Smallest Item = 15-6 = 9

Co – efficient of Range = Largest Items – Smallest Items

Largest Items + Smallest Items – 9 15-6 9 _=a43