Question

Consider the following sample of five measurements.

2,3,1,0,7

a. Calculate the range, s^2 , and s.

range=________

s^2=__________

s=_____________

b.add 2 to each measurement and repeat part a.

range=_______

s^2=_________

s=____________

c. Subtract 5 from each measurement and repeat part a.

range=_________

s^2=__________

s=___________

d. Considering your answers to parts ​a, b, and ​c, what seems to be the effect on the variability of a data set by adding the same number to or subtracting the same number from each​ measurement?

A. There is no effect on the variability.

B.The variability is multiplied by the amount added to or subtracted from each measurement.

C.The variability is increased by the amount added to each measurement.

D.The variability is decreased by the amount subtracted from each measurement.

  

Answer 1

Solution:
Sample is (2,3,1,0,7)
Range = (7-0) = 8
S^2 = summation(Xi-mean)^2 / (n-1)
mean = (2+3+1+0+7)/5 = 2.6

X	Xi-mean	(Xi-mean)^2
2	-0.6	0.36
3	0.4	0.16
1	-1.6	2.56
0	-2.6	6.76
7	4.4	19.36

S^2 = (0.36+0.16+2.56+6.76+19.36)/4 = 29.2/4 = 7.3
S = sqrt(7.3) = 2.7018

Solution(b)
add 2 in each sample
4,5,3,2,9
Range = (9-2) = 7
Mean = 4.6

X	Xi-mean	(Xi-mean)^2
4	-0.6	0.36
5	0.4	0.16
3	-1.6	2.56
2	-2.6	6.76
9	4.4	19.36

S^2 = 29.2/4 = 7.3
S = sqrt(7.3) = 2.7018

Solution(c)
Subtract 5 from each sample
-1,0,-2,-3,4
Range = 4-(-3) = 7
Mean = -0.4

X	Xi-mean	(Xi-mean)^2
-1	-0.6	0.36
0	0.4	0.16
-2	-1.6	2.56
-3	-2.6	6.76
4	4.4	19.36

S^2 = (29.2/4) = 7.3
S= 2.7018
Solution(d)
As we can see that there is no variability.