The trend thinner beauty pageant winners has generated charges that the contest

Question

The trend thinner beauty pageant winners has generated charges that the contest encourages unhealthy diet habits among young women. Listed below are body mass indexes (BMI) for beauty pageant winners from two different time periods. Find the coefficient of variation for each of the two sets of data, then compare the variation. BMI (from the 1920s and 1930s):20.3 219 22.1 22.3 203 18.8 18.9 19.4 18.3 19.1 BMI (from recent winners):19.5 20 4 197 20 2 17 7 178 191 189 175 168 The coefficient of variation for the BMI's of beauty pageant winners from the 1920s and 1930s is % (Round to one decimal place as needed)

Explanation / Answer

coefficient of variation for any dataset is given as cv=sigma/u where u is the mean of the data set and sigma is the standard deviation of the dataset.

now we have two datasets

BMI (from 1920's and 1930's): 20.3 21.9 22.1 22.3 20.3 18.8 18.9 19.4 18.3 19.1

u for this dataset is u=(20.3+21.9+...+18.3+19.1)/10=20.140

sigma for this dataset=sqrt[{(20.3-20.140)2+(21.9-20.14)2+....+(18.3-20.14)2+(19.1-20.14)2}/9]=1.491

so coefficient of variation is =1.491/20.14=0.074=0.1 [answer] [rounded to 1 decimal]

another data set

BMI (from recent winners) :

19.5
20.4
19.7
20.2
17.7
17.8
19.1
18.9
17.5
16.8

so mean=u=(19.5+20.4+...+17.5+16.8)/10=18.76

standard deviation=sigma=sqrt[{(19.5-18.76)2+(20.4-18.76)2+...+(17.5-18.76)2+(16.8-18.76)2}/9]=1.238

so coefficient of variation=cv=1.238/18.76=0.06599=0.1 [answer] [rounded to 1 decimal]

so both the cvs are same.

hence there is no difference in the dispersion between the two datasets

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