Example 15

Transcript

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.) = 𝑺𝒕𝒂𝒏𝒅𝒂𝒓𝒅 𝑫𝒆𝒗𝒊𝒂𝒕𝒊𝒐𝒏﷮𝑴𝒆𝒂𝒏﷯ × 100 Variance of height = 127.69 cm2 Standard deviation of height = ﷮𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒﷯ = ﷮127.69﷯ = ﷮127.69﷯ = ﷮ 12769﷮100﷯﷯ = ﷮ 113﷯2﷮ 10﷯2﷯﷯ = ﷮ 113﷮10﷯﷯﷮2﷯﷯ = 113﷮10﷯﷯ = 11.3 cm Variance of weight = 23.1361 kg2 Standard deviation of weight (σweight) = ﷮𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒﷯ = ﷮23.1361﷯ = ﷮ 231361﷮10000﷯﷯ = ﷮ 231361﷮10000﷯﷯ = ﷮ 481﷯2﷮ 100﷯2﷯﷯ = ﷮ 481﷮100﷯﷯﷮2﷯﷯ = 481﷮100﷯﷯ = 4.81 kg Now, calculating Coefficient of variation C.V. in height = 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 ℎ𝑒𝑖𝑔ℎ𝑡 ﷮𝑀𝑒𝑎𝑛 ℎ𝑒𝑖𝑔ℎ𝑡﷯ × 100 = 11.3﷮162.6﷯ × 100 = 6.95 C.V. in weight = 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑤𝑒𝑖𝑔ℎ𝑡 ﷮𝑀𝑒𝑎𝑛 𝑤𝑒𝑖𝑔ℎ𝑡﷯ × 100 = 4.81﷮52.36﷯ × 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