In this problem, we the effect on deviation of multiplying each data value in a

Question

In this problem, we the effect on deviation of multiplying each data value in a data set by the same constant Consider the data set 4, 8, 5, 5. 16. Standard. (a) use the defining formula, the computation formula, or a calculator to compute s. s = __________ (b) Multiply each data value by 4 to obtain the new data set 16, 32, 20, 20, 64.compute s. s = _____________ (c) Compare the results of parts (a) and (b) In general, how does the standard deviation change if each data value is multiplied by a constant c? Multiplying each data value by the same constant c results in the standard deviation increasing by c units. Multiplying each data value by the same constant c results in the standard deviation being [c] times smaller. Multiplying each data value by the same constant c results in the standard deviation being [c] times as large. Multiplying each data value by the same constant c results in the standard deviation remaining the same.

Explanation / Answer

(a)

Using the STDEV function in EXCEL we find the standard deviation for the given data set to be 4.9.

s = 4.9

(b)

After multiplying each data value by 4 , we find the standard deviation of the new data set to be 19.7

(c)

Here we can see that the standard deviation has become 4 times of the previous one. hence the correct option would be ,

Multiplying each data value by the same constant c results in the standard deviation being |c| times as large.

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