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

Slide6.JPG Slide7.JPG

  1. Chapter 15 Class 11 Statistics
  2. Serial order wise
Ask Download


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

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 7 years. He provides courses for Mathematics and Science from Class 6 to 12. You can learn personally from here https://www.teachoo.com/premium/maths-and-science-classes/.