The table below summarizes the lean body mass (in kg) and metabolic rate (in cal

Question

The table below summarizes the lean body mass (in kg) and metabolic rate (in calories per day) for a sample of 12 women. Compute the coefficient of variation for each variable and determine which of the two variables exhibits more variability in this sample. Use Chebychev's Inequality to obtain an interval guaranteed to contain at least 75% of the lean body mass values of the women in the sample. Based on the summary in the above table, can you verify that your conclusion is correct? How can you tell?

Explanation / Answer

a) as coefficient of variation =(mean/std deviation)

hence COV for lean body mass =8.1/42.1 =0.1924

and COV for metabolic rate =188.3/1235.1=0.1525

from above it is seen that lean body mass exhibits more variation.

b)from chebychev at leat 75% values lie with in 2 std deviation from mean.

hence interval =mean +/- 2*std deviation =(25.9 ; 58.3)

by looking at the summary table, our interval contains all the values as interval upper value is higher then maximum value,and interval lower value is lower then minimum value

therefore above interval contains at least 75% values

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