Elementary statistics Q8 Please explain well 8) of two persons on a reducing die

Question

Elementary statistics Q8 Please explain well
8) of two persons on a reducing diet, the first belongs to an age group for which the mean weight is 142 pounds with a standard deviation of 15 pounds, and the second belongs to an age group for which the mean weight is 138 pounds with a standard deviation of 13 pounds. If their respective weights are 161 pounds and 154 pounds, which of the two is more seriously overweight for his or her age group? (use z-scores and round to the hundredths, if necessary) Mean of Grouped Data sz n-1 Sample Standard Deviation s Sample Variance: n-1 Shortcut Formula for Variance: s 202 -CX n (n-1) Shortcut Formula for the Standard Deviation s n(n-1) Formula for Converting to Standard Units

Explanation / Answer

In order to compare which one is more seriously overweight according to their age groups we need to bring them to the same scale. So we calculate both the z scores according to their age group's mean and standard deviation:

Z score for fist individual with weight 161 of age group having mean weight = 142 and standard deviation= 15 = 1.267

Z score for fist individual with weight 154 of age group having mean weight = 138 and standard deviation= 13 = 1.231

From the z scores we can see that first individual has more over weight than second one when brought to the standard normal distribution scale whose mean is 0 and standard deviation is 1

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