Range, Applied Statistics

Range

Official Exports Target 2000-2001

Product

($ million)

Plantation

500

Agriculture and Allied Products

2,255

Marine Products

650

Ores & Minerals

869

Leather & Leather manufactures

1,490

Gems & Jewelry

3,455

Sports goods

37

Chemical & Related project goods

2,168

Engineering & Related project goods

2,500

Electronics

375

Textiles Including Handicrafts & Carpets

7,400

Raw Cotton

170

Petroleum Products

269

Total

22,138

Product-wise targets vary from $37 million for sports goods to $7,400 million for Textiles including handicrafts and carpets.

Range is the simplest measure of dispersion.

Range  = Value of highest data point - Value of lowest data point

Hence we need to know the value of only two data points to calculate the range.

In the case of India's export targets for 2000-2001, the range of individual product targets is 7,400 - 37 = $7,363 million. However, if we exclude the export target for Textiles (including handicrafts and carpets) the range becomes 3455 - 37 = $3418 million. Hence the exclusion of a single data point has caused the range to decline by 53.6%. This shows how extreme data points can strongly influence the range.

In the above case, this undue influence of one item may be justified on the grounds that the particular item, export target for Textiles (including handicrafts and carpets) is the single largest item making up a third of the total target.

However, consider the following set of data points: 100, 100, 100, 100, 0. The range is 100 - 0 = 100. However, if we exclude the data point 0, the range is 100 - 100 = 0. Hence the exclusion of a data point 0 which contributes nothing to the total, changes the range from 100 to 0.

The main drawback of the range as a measure of dispersion is that it is influenced by only two data points - the largest and the smallest. No other data point is involved in the calculation of the range. In fact, even if other data points are changed they will not influence the range (provided, of course, that none of the new data points exceed the value of the largest data point or falls below the smallest data point).

There are other modified range measures of dispersion like the interquartile range, but all suffer a drawback that they take into account only the two data points used in their calculation

 

Posted Date: 9/14/2012 2:47:58 AM | Location : United States







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