Example 15 - Values are calculated in respect of heights, weights - Examples

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  1. Chapter 15 Class 11 Statistics
  2. Serial order wise
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Example 15 The following values are calculated in respect of heights and weights of the students of a section of Class XI : Can we say that the weights show greater variation than the heights? To compare the variation, we have to calculate coefficient of variation Coefficient of variation(C.V.) = ๐‘บ๐’•๐’‚๐’๐’…๐’‚๐’“๐’… ๐‘ซ๐’†๐’—๐’Š๐’‚๐’•๐’Š๐’๐’๏ทฎ๐‘ด๐’†๐’‚๐’๏ทฏ ร— 100 Variance of height = 127.69 cm2 Standard deviation of height = ๏ทฎ๐‘‰๐‘Ž๐‘Ÿ๐‘–๐‘Ž๐‘›๐‘๐‘’๏ทฏ = ๏ทฎ127.69๏ทฏ = ๏ทฎ127.69๏ทฏ = ๏ทฎ 12769๏ทฎ100๏ทฏ๏ทฏ = ๏ทฎ 113๏ทฏ2๏ทฎ 10๏ทฏ2๏ทฏ๏ทฏ = ๏ทฎ 113๏ทฎ10๏ทฏ๏ทฏ๏ทฎ2๏ทฏ๏ทฏ = 113๏ทฎ10๏ทฏ๏ทฏ = 11.3 cm Variance of weight = 23.1361 kg2 Standard deviation of weight (ฯƒweight) = ๏ทฎ๐‘‰๐‘Ž๐‘Ÿ๐‘–๐‘Ž๐‘›๐‘๐‘’๏ทฏ = ๏ทฎ23.1361๏ทฏ = ๏ทฎ 231361๏ทฎ10000๏ทฏ๏ทฏ = ๏ทฎ 231361๏ทฎ10000๏ทฏ๏ทฏ = ๏ทฎ 481๏ทฏ2๏ทฎ 100๏ทฏ2๏ทฏ๏ทฏ = ๏ทฎ 481๏ทฎ100๏ทฏ๏ทฏ๏ทฎ2๏ทฏ๏ทฏ = 481๏ทฎ100๏ทฏ๏ทฏ = 4.81 kg Now, calculating Coefficient of variation C.V. in height = ๐‘†๐‘ก๐‘Ž๐‘›๐‘‘๐‘Ž๐‘Ÿ๐‘‘ ๐‘‘๐‘’๐‘ฃ๐‘–๐‘Ž๐‘ก๐‘–๐‘œ๐‘› ๐‘œ๐‘“ โ„Ž๐‘’๐‘–๐‘”โ„Ž๐‘ก ๏ทฎ๐‘€๐‘’๐‘Ž๐‘› โ„Ž๐‘’๐‘–๐‘”โ„Ž๐‘ก๏ทฏ ร— 100 = 11.3๏ทฎ162.6๏ทฏ ร— 100 = 6.95 C.V. in weight = ๐‘†๐‘ก๐‘Ž๐‘›๐‘‘๐‘Ž๐‘Ÿ๐‘‘ ๐‘‘๐‘’๐‘ฃ๐‘–๐‘Ž๐‘ก๐‘–๐‘œ๐‘› ๐‘œ๐‘“ ๐‘ค๐‘’๐‘–๐‘”โ„Ž๐‘ก ๏ทฎ๐‘€๐‘’๐‘Ž๐‘› ๐‘ค๐‘’๐‘–๐‘”โ„Ž๐‘ก๏ทฏ ร— 100 = 4.81๏ทฎ52.36๏ทฏ ร— 100 = 9.18 Since, C.V. in weights is greater than the C.V. in heights Therefore, we can say that weights show more variability than heights

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