The average weight of a group of people is 156 pounds and the SD is 25 pounds. A statistician wants to transform the weights so that the transformed weights have an average of 100 pounds and an SD of 10 pounds. Fill in the blanks; both blanks must be filled in correctly for credit.
Note: the first blank corresponds to the higher entry box; the second blank corresponds to the lower entry box.
One way for the statistician to get the transformation that she wants is to multiply all the weights by _____________, and then add _____________ to the resulting values.
One way for the statistician to get the transformation that she wants is to multiply all the weights by the ratio of the desired standard deviation to the current standard deviation, and then subtract the product of the ratio and the current average from the resulting values.
To find the ratio of the desired standard deviation to the current standard deviation, we divide the desired standard deviation by the current standard deviation:
Ratio = (Desired SD) / (Current SD) = 10 / 25 = 0.4
To find the product of the ratio and the current average, we multiply the ratio by the current average:
Product = (Ratio) * (Current Average) = 0.4 * 156 = 62.4
Therefore, the blank would be filled as follows:
One way for the statistician to get the transformation that she wants is to multiply all the weights by 0.4, and then subtract 62.4 from the resulting values.