Name ___________________________________________ Date ______________________
Algebra 2
Test Review: Statistics
1. Descriptive statistics are shown for a data set below.
Mean = 77; Absolute Mean Deviation = 16; Variance = 420.3; Standard Deviation = 20.5
Does the mean accurately describe the behavior of this data? Explain your reasoning.
2. At the Chips Factory, bags of chips are filled by a machine into 6-ounce bags. It is difficult to
fill a bag with exactly 6 ounces of chips every time. For the past month, the manager of the
Chips factory has been trying to determine which machines can fill bags of chips the most
accurately. The manager collected the standard deviation of sample chip bags each week for
each of his machines.
Machine 1
Week
1
0.14
Week
2
0.11
Week
3
0.2
Week
4
0.1
Machine 2
0.2
.19
.1
.1
Machine 3
0.15
0.18
0.15
0.12
Machine 4
0.1
0.3
0.1
0.13
Compare and contrast the standard deviations for each machine. The manager needs to
choose one machine to remove. Which machine should he remove? Explain your reasoning.
3. The data set shown has a mean of 31.83 and a standard deviation of 3.76, rounded to the
nearest hundredth. 26, 29,32,33,35,36
Which of these data points have a z-score greater than 0.4? Show your work.
4. Amy took the ACT and scored a 27 on the mathematics portion of the test. Her friend
Stephanie scored a 660 on the mathematics portion of her SAT. Both tests have scores that
are normally distributed. For the SAT, the mean was 515 and the standard deviation was
116. For the ACT, the mean was 21 and the standard deviation was 5.3. Whose achievement
was higher on the mathematics portion?
Name ___________________________________________ Date ______________________
Algebra 2
5. In a set of scores, a raw score of 72 has a z-score of 1 and a raw score of 76 has a z-score of 2.
What is the mean score? ____________ What is the standard deviation? _____________
6. Given two different sets of data: Set 1={85, 92, 88,80, 91, 20} and Set 2={85, 92, 88, 80, 91, 74}.
Which of the following statements is true?
a. Both sets of data contain an outlier.
b. The standard deviation for set 1 is greater than the standard deviation for set 2.
c. The mean absolute deviation for set 1 is larger than the standard deviation for set 1.
d. The mean absolute deviation is larger for set 2 than the standard deviation for set 2.
7. Which of the following data sets has the smallest standard deviation?
a. a. 51,52,52,50,50,53,49
b. 55,58,52,50,22,35,42
c. 37,41,33,31,12,24,43
d. 28,34,24,21,8,36,13
8. Explain why the sum of the deviations is always zero.
9. Which measure of dispersion is more affected by outliers: mean absolute deviation or
standard deviation? Explain your reasoning.
10. The College of Knowledge gives an admission qualifying exam. The results are normally
distributed with a mean of 500 and a standard deviation of 100. The admissions department
would like to accept only students who score in the 65th percentile or better. Complete the
chart below, and then determine which students qualify for admission.
Student Score
z-score
Percentile
530
570
650
800
540
11. Given a normally distributed data set of 400 observations measuring newborn weights, what
is the approximate number of observations that fall within 1 standard deviation of the mean?
Name ___________________________________________ Date ______________________
Algebra 2
12. The table below shows the heights of all fourth-grade students in a particular school, and the
frequency of each height. Use the table to answer the following:
Height
130
131
132
133
134
135
136
137
138
(cm)
2
7
9
20
38
18
12
10
5
Frequency
a.
Identify the mean, median, and mode of the data.
b. Identify two values that could be added to the existing data set that would not affect the
mean, median, or mode. How did you determine these values?
c. What percentage of the students is shorter than 135 cm?
d. Does this data appear to be normally distributed? Explain why or why not.
13. The breaking distance for a Krazy-Car traveling at 50 mph is normally distributed with a
mean of 50 ft. and a standard deviation of 5 ft. Answer the following:

What is the likelihood a Krazy-Car will take more than 63 ft. to stop?

What is the probability a Krazy-Car will stop between 45 ft. and 55 ft.?

What percent of the time will a Krazy-Car stop between 35 and 55 ft?

What is the likelihood a Krazy-Car will take less than 49 ft. to stop?