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Kelly Bell gets quiz grades of 65, 83, 80, and 90. She gets a 92 on her final ex

ID: 3300375 • Letter: K

Question

Kelly Bell gets quiz grades of 65, 83, 80, and 90. She gets a 92 on her final exam. Find the weighted mean if the quizzes each count for 15% and the final counts for 40% of the final grade. If the heights of women have a mean of 63.6 in. and a standard deviation of 2.5 in., what can you conclude from the Chebyshev's theorem about the percentage of women between 58.6 in. and 68.6 in.? (Answer: Percentage is at least 75%.) In each of the following, describe how the range and standard deviation of a data set are affected. a. The same constant k is added to each value of the data set. b. Each value of the data set is multiplied by the same constant k.

Explanation / Answer

3) a) here as Range =(maximum -mimimum)

when a number k is added to each element;

new range =(maximum+k -mimimum-k) =(maximum -mimimum) =old range

therefore range does not get affected.

for a number k is added to each element;; new mean value will become mean+k.

as variance is proportional to (xi -mean)2

therefore new varaince should be proportional to (xi+k-mean-k)2 =(xi-k)2  which is equal to old variance

as variance not got affected therefore std deviation does not get affected.

b)

after multiplying each element with k;

new range =(k*maximum-k*minimum) =k*old range

therefore new range will become k times old range.

similarly variance is proportional to (kxi-k*mean)2  =k2* (xi-mean)2 =k2*old variance

hence new std deviation =k*old std deviation

therefore new std deviation will become k times old std deviation