1,2 In this problem. we explore the effect on the standard deviation of adding t
ID: 3041855 • Letter: 1
Question
1,2
In this problem. we explore the effect on the standard deviation of adding the same constant to each data value in a data set. Consider the followring data selt. 17, 11, 10, 14, 9 (a) Use the defining formula, the computation formula, or a calculator to compute s. (Enter your answer to one decimal place.) b) Add 7 to each data value to get the new data set 24, 18, 17, 21. 16. Compute s. (Enter your answer to one decimal placo.) (c) Compare the results of parts (a) and (b). In general, how do you think the standard deviation of a data set changes if the same constant is added to each data value? O Adding the same constant c to each data value results in the standard deviation remaining the same. O Adding the same constant c to each data value results in the standard deviation increasing by c units O Adding the same constant c to each data value results in the standard deviation decreasing by c units O There is no distinct pattern when the same constant is added to each data value in a set. Given the sample dats ri 21 17 15 30 25 Find the range. (b) Venify that Bx 108 and x2,480. at and samps standard deviation s. Chound your ansvars to tuo decimal places) (c) Use the results of part (b) and appropriate computation formulas to computo the sample veriance to two decimal places.) formulas to compute the sample veriance s and sample standard deviation s. (Round your anawers ulation of all r values. Compute the population variance + and population standard deviation . Round your answers to two decimal places.)Explanation / Answer
(1) The data set is 17, 11, 10, 14, 9.
(a) s = standard deviation = 3.3.
(b) s = 3.3
(c) 1st Option is correct, that is, the SD remains the same even if we add a constant to each value in the dataset.
(2) The data set is 21, 17, 15, 30, 25.
(a) Range = 30 - 15 = 15.
(b) 21 + 17 + 15 + 30 + 25 = 108.
212 + 172 + 152 + 302 + 252 = 2480.
(c) Using computational formulas, variance = s2 = 36.80.
sd = s = 6.07.
(d) Using defining formulas, variance = s2 = 36.80.
sd = s = 6.07.
(e) Population variance = 29.44.
Population standard deviation = 5.43.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.