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Math 2
Name _________________________ _______________
Statistics Review
Date________________
1.
The standard deviation of 18 measurements of people’s weights (in pounds) is computed to be 6.4 Calculate the variance of these
measurements.
2.
The following is a box plot of the weights (in pounds) of a sample of 240 sophomores in Osborne High School.
About 60 of the student weights are above:
a)
b)
c)
d)
92
102
112
122
lbs.
lbs.
lbs.
lbs.
3.
Salaries of professional basketball players take on a left-skewed distribution. If we were to take both the mean and median of this
distribution, what would be true about the relationship between these two measures?
(a) Mean salary is equal to median salary
(b) Mean salary is less than median salary
(c) Mean salary is greater than median salary
(d) There is not enough information provided to answer.
4.
In the accompanying display, which has the larger mean and which has the larger standard deviation?
(a) Larger mean, A; larger standard deviation, A
(b) Larger mean, A; larger standard deviation, B
(c) Larger mean, B; larger standard deviation, A
(d) Larger mean, B; larger standard deviation, B
5. If each score in a set of scores were increased by 6 points, how would this affect the
mean and the standard deviation?
(a) Mean would increase by 6; standard deviation would remain the same.
(b) Mean would remain the same; standard deviation would increase by 6.
(c) Mean would remain the same; standard deviation would increase by 36.
(d) Mean would increase by 6; standard deviation would increase by 6.
6. William made a 78 on an exam where the class grades were normally distributed with an average of 86 and a standard deviation of
4. Which is true about William‘s score in relation to the rest of the class?
(a) William‘s score is above the 50th percentile of class scores
(b) William‘s score was below the 2nd percentile of class scores
(c) William‘s score was 2 standard deviations below the mean
(d) William‘s score was 2 standard deviations above the mean
7. Calculate the mean, median, mode, mean absolute deviation, variance, standard deviation, range and Inter-quartile range for the
two data different data sets.
The scores from the last quiz of Mr. Pratt’s math class:
71
88
93
99
78
78
60
mean: _________________
median:
_________________
mode:
_________________
MAD:
_________________
variance:
_________________
standard deviation:
_________________
range:
_________________
Interquartile range:
_________________
Label the headings of the columns and show your work. MAD
Label the headings of the columns and show your work. Standard Deviation
The scores from the last quiz of Ms. Amaya’s math class:
84
77
74
96
84
77
75
mean: _________________
median:
_________________
mode:
_________________
MAD:
_________________
variance:
_________________
standard deviation:
_________________
range:
_________________
Interquartile range: _________________
Label the headings of the columns and show your work. MAD
Label the headings of the columns and show your work. Standard Deviation
Mr. Nicol’s math class had an average of 82 on the unit test with a standard deviation of 3.8. Mrs. McNelis’ math class had an
average of 82 on the same unit test with a standard deviation of 5.9. Which is true in comparing the performance of the two
classes?
(a) Both classes did equally well
(b) Mr. Nicol’s class did better than Mrs. McNelis’ class
(c) Mr. Nicol’s class did worse than Mrs. McNelis’ class
(d) Mr. Nicol’s class had less spread in the scores than Mrs. McNelis’ class
9.
Given the histogram below, calculate the mean and standard deviation. Use these values to determine whether the
distribution could be normal.
Histogram
Collection 1
6
5
4
Count
8.
3
2
1
38
40
42
44
46
48
data
50
52
54
56
Label the headings of the columns and show your work. Standard Deviation
Is the distribution Normal? _____________________ Explain:
____________________________________________________________________________________________________
____________________________________________________________________________________________________
_________________________
10.
A small engineering company owned by Dr. Hall has five employees with the annual salaries given in thousands of
dollars:
Clerk: 38
Engineer B: 85
Draftsman: 46
Engineer C: 96
Engineer A: 78
Dr. Hall (owner): 600
(a) What is the Mean and Median salary for the 5 employees only?
(b) If Dr. Hall’s salary is added to the other five employees, what are the new Mean and new Median salaries for the company?
(c) What is the best measure of central tendency if Dr. Hall’s salary is added to the list? Explain your answer in one sentence.
11.
Lewis earned 84 on his biology midterm and 82 on his history midterm. In the biology class the mean score was 79 with a
standard deviation of 5. In the history class the mean score was 76 with a standard deviation of 3.
(a) For each midterm, how many standard deviations is Lewis from the class mean score.
Biology:
History:
(b) On which test did he do better compared to the rest of the class? Explain your answer.
12. On one measure of attractiveness, scores are normally distributed with a mean of 3.93 and a standard deviation of .75. Find the
probability of randomly selecting a subject with a measure of attractiveness that is greater than 3.18.
13. A manufacturer makes small screws that fit into eyeglass frames. The diameter of the
screws must be between 0.95 mm and 1.15 mm. Quality control tests indicate that the
diameters of the screws produced are normally distributed with mean 1.05 mm and
standard deviation 0.05 mm.
a. What percent of the screws have diameters smaller than 0.95 mm?
b. What percent of the screws have diameters greater than 1.15 mm?
c. What percent of the screws have diameters that are within the 0.95 to 1.15 mm range?
14. A large random sample was taken from a normally distributed population.
The sample mean is 3 feet, the sample standard deviation is 0.5 feet, and the
population size is 850,000. Determine the number of data values in
the population that are greater than 4 feet.
A.
B.
C.
D.
9,690
21,250
38,760
77,520
15. The table below displays the approximate base salaries of the 13 members of the Miami Heat basketball team for the year
2005 salaries for Miami Heat Players (in millions of dollars). SHOW YOUR WORK!!
Player
Salary
Player
Salary
Shaquille
O’Neal
27.7
Christian
Laettner
1.10
Eddie Jones
13.46
Shandon
Anderson
0.87
Dwyane Wade
2.83
Keyon Dooling
0.75
Damon Jones
2.50
Udonis Haslem
0.62
Michael Doleac
2.40
Alonzo
Mourning
0.33
Rasual Butler
1.20
Dorell Wright
1.15
Qyntel Woods
1.13
(a) Calculate the mean salary for the players on the Miami Heat in the year 2005. _______________________
(b) Calculate the standard deviation of the Miami Heat salaries. _______________________
Variance: _______________________________________
Standard Deviation: ________________________________________
15.
If every player on the Miami Heat basketball team received a bonus of $12 million calculate the:
(a) New Mean: ___________________________________________________________________________
(b) New Standard Deviation: ________________________________________________________________
16. If the salary of each of the players tripled calculate:
(a) New Mean: ___________________________________________________________________________
(b) Standard Deviation: ________________________________________________________________
17. Determine the five-number summary for the salaries of the Miami Heat basketball team for 2005.
Median: ________ Q1: ________
Q3: ________
Minimum: ________ Maximum: ________
18. Display the distribution of the Miami Heat salaries for 2005 in a boxplot.
19. Calculate the Interquartile range (IQR): ________________________________________________
20. How much of the data is contained in the IQR: ________________________________
21. If you were a sports writer for the Miami Herald would you report the team salary using a mean or a median? Explain your
decision.
__________________________________________________________________________________________________
__________________________________________________________________________________________________