In this problem, we explore the effect on the standard deviation of multiplying
ID: 3127802 • Letter: I
Question
In this problem, we explore the effect on the standard deviation of multiplying each data value in a data set by the same constant. Consider the data set 10,16,10,10,11.
a.) Use athe definding formula, the computation formula or calculator to compute s. round answer to one decimal
s=
b.) Multiply each data value by 8 to obtain teh new data set 80,128,80.80,88, compute s round your answer to one decimal place.
Given 1 mile equals close to 1.6klometer, what is the standard deciation in kilometers, enter your answer to two decimal places.
Explanation / Answer
a)
Getting the mean, X,
X = Sum(x) / n
Summing the items, Sum(x) = 57
As n = 5
Thus,
X = 11.4
Setting up tables,
x x - X (x - X)^2
10 -1.4 1.96
16 4.6 21.16
10 -1.4 1.96
10 -1.4 1.96
11 -0.4 0.16
Thus, Sum(x - X)^2 = 27.2
Thus, as
s^2 = Sum(x - X)^2 / (n - 1)
As n = 5
s^2 = 6.8
Thus,
s = 2.607680962 = 2.6 [ANSWER]
*********************
b)
Getting the mean, X,
X = Sum(x) / n
Summing the items, Sum(x) = 456
As n = 5
Thus,
X = 91.2
Setting up tables,
x x - X (x - X)^2
80 -11.2 125.44
128 36.8 1354.24
80 -11.2 125.44
80 -11.2 125.44
88 -3.2 10.24
Thus, Sum(x - X)^2 = 1740.8
Thus, as
s^2 = Sum(x - X)^2 / (n - 1)
As n = 5
s^2 = 435.2
Thus,
s = 20.8614477 = 20.9 [ANSWER]
*************************
C)
s - 20.861 mi = 20.861*1.6 km = 33.38 km [ANSWER]
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.