Range
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This document discusses measures of dispersion, or variation, in data sets. It describes absolute and relative measures of dispersion. Absolute measures give the dispersion in the same units as the original data but cannot be used to compare different data sets. Relative measures are dimensionless and can be used to compare dispersion across data sets. The document then discusses the range as the simplest measure of absolute dispersion. The range is defined as the difference between the maximum and minimum values in a data set. It also defines the coefficient of range, which normalizes the range as a percentage to allow comparison between data sets. Two examples are given to demonstrate calculating the range and coefficient of range.
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Deviation, Fluctuation, Spread or variability of data.
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Range
- 1. RANGE NADEEM UDDIN ASSOCIATE PROFESSOR OF STATISTICS HTTPS://WWW.SLIDESHARE.NET/NADEEMUDDIN17 HTTPS://NADEEMSTATS.WORDPRESS.COM/LISTOFBOOKS/
- 2. Absolute Measure of Dispersion: Gives an idea about the amount of dispersion/spread in a set of observations. These quantities measures the dispersion in the same units as the units of original data. Absolute measures cannot be used to compare the variation of two or more series/ data set. A measure of absolute dispersion does not in itself, tell whether the variation is large or small. Relative Measure of Dispersion: Relative measures are not expressed in units but it is a pure number. It is useful for compairing two or more sets of data.
- 3. Range: The range is the simplest measure of dispersion; it is the difference between the maximum and the minimum values in a data set. Range = Maximum Value − Minimum Value. Coefficient of Range 100 Value Min. Value Max. Value Min. Value Max.
- 4. Example-1: The marks obtained by 10 students are given below 36, 45, 32, 50, 41, 39, 49, 32, 46, 38 find (a) Range (b) Co-efficient of dispersion Solution: (a) R = Max.Value – Min.Value = 50 – 32 = 18 marks 100 . . . . V Min V Max V Min V Max 50 32 100 21.95% 50 32 (b) Co-efficient of dispersion
- 5. Example-2: Find range and coefficient of Dispersion. C.B F 4 – 8 5 8 – 12 10 12 – 16 15 16 – 20 8 20 – 24 6 Solution: R = U.C.B of last interval – L.C.B of first interval R = 24 – 4 = 20 Coefficient of dispersion % 43 . 71 100 4 24 4 24