SOL A.9
The student, given a set of data, will interpret variation in
real-world contexts and calculate and interpret mean absolute
deviation, standard deviation, and z-scores.
1. A data set has a mean of 34 and a standard deviation of 4.5. An
element in the data set has a z-score of -1.2.
a)Without doing a calculation, state whether this element is less than, equal to, or greater than
34.
b)Determine the element of the data set.
2.
A data set shown has a mean of 60 and a standard deviation of 9.9, rounded to the nearest
tenth.
{48, 51, 55, 60, 72, 74}
How many of these data points have a z-score greater than -1?
Which number in the data set has a z-score of 0?
3.
Mean
Find the values of the element for each if you are given:
Standard Deviation
Z-Score
Element
60
11
1.8
______
58
12
2.1
______
55
13
1.4
______
57
10
2.5
______
4.
This table shows data on the number of ROAR’s for 4 math classes and for one student in the
class:
Mean for class
Rick
17
Standard
deviation
3
Student
z-score
1.1
William
14
4
1.5
James
13
7
2.0
Owen
15
5
1.8
Which student above has collected the
most ROAR’s? _____________
5. This table shows data on the amount of money made from a fundraiser for 4 math classes and for
one student in the class:
Mean for class
Standard
deviation
5
Student
z-score
1.9
Victor
60
Ashley
62
12
1.5
Carrie
13
7
1.3
Dave
65
8
2.1
Which student above raised the most money?
6. The mean of a data set is 45. The Z-score for data point “a” is 0. The z-score for data point “b” is 0.2.
Which are the possible values of data point “a” and “b”?
A. a= 0 b = 47.2
B. a=0 and b = 44.2
C. a = 45 and b = 45.8
D. a = 45 and b = 44.2
7. Statistical information for a data set is given.



The mean of the data set is 30.
The standard deviation for the data set is 3
The Z-score for a data point is 2.25
The data point must be between:
A. 18 ≤ x < 24
B. 24 ≤ x < 30
C. 30 ≤ x < 36
D. 36 ≤ x < 42