Download Math I Unit 2: Statistics Review Questions Name ______ The

Math I Unit 2: Statistics Review Questions
Name ______________________________
1. The following data represents the Algebra test scores of 20 students:
29, 31, 67, 67, 69, 70, 71, 72, 75, 77, 78, 80, 83, 85, 87, 90, 90, 91, 91, 93
a) What is the mean: ___________________, mode: __________________, and median: _________________,?
b) Create a box-plot
c) What is the interquartile range?
d) What is the standard deviation?
e) Suppose that a 21st score of a 5 on a test is added. Which of ‘a’ is likely to change the most?
Will the standard deviation increase or decrease?
f) Describe the shape, center and spread of this data.
2. Describe the shape of the following distributions. Use words like skewed to the left (less numbers on the
left), skewed to the right (less numbers to the right), normal (evenly distributed).
A: ____________________
C: ____________________
B: ____________________
3. Use the following box-plot of 120 bowlers to answer the questions
a) What is the interquartile range?
d) What is the range?
b) What is the maximum?
c) What is the minimum?
e) How many people got at most 95?
4. A set of data has a mean of 56.7 and a standard deviation of 2.5:
What would the new mean and new standard deviation be if each of the data is increased by 5?
5. The data below shows the ages of teachers: 23, 25, 25, 27, 29, 30, 31, 32, 33, 34, 36, 37, 40, 41, 42, 43, 55
a) What measure of spread is more appropriate for this data (mean, mode, median, or standard deviation?)
b) Describe the shape of this data. (Skew, Normal, Random)
6. A teacher interviewed 200 students and found the following results:
a) How many senior males did the teacher interview?
b) If the student was a sophomore, what gender was it more likely to be?
Male Female
Sophomore
Junior
Senior
.2
.1
.25
.1
.25
.1
c) How many more female juniors were there than male juniors?
7.
The following are test scores of a Biology test:
55, 59, 60, 61, 65, 65, 65, 70, 72, 73, 74, 76, 77, 78, 82, 88, 93, 94, 95
a) Find MEAN: _______________, MODE: _______________, MEDIAN: _______________, RANGE: _______
b) Create a box-plot
c) What is the interquartile range?
d) What is the standard deviation?
e) Suppose that a 20th score of a 5 on a test is added. Which of ‘a’ is likely to change the most? Will the standard
deviation increase or decrease?
8. Use the following box-plot of answers to 80 people to answer the questions
a) What is the interquartile range?
b) What is the maximum and minimum?
c) How many people got at least 16?
9. A set of data has a mean of 44.7 and a standard deviation of 1.3: What would the new mean and new
standard deviation be if each of the data is decreased by 3?
23500, 26000, 28000, 29000, 32500, 36500, 38500,
42200, 55000, 58500, 62000, 67000, 112200
10. The data shows the household income:
a) What measure of spread is more appropriate for this data (mean, mode, median, or standard deviation?)
b) Are there any outliers? (Explain…)
c) Describe the shape of this data.
d) Suppose that a millionaire is added to the data set, which measure of spread will increase the most?
11. 400 people were surveyed. Each person was asked whether he or she prefers Drama or Comedy movies.
The results are shown in the relative frequency table below:
a) How many more people prefer drama than comedy?
Age
Drama
Comedy
Total
21-30 .25
.30
.55
31-40 .15
.06
.21
b) How many more 21-30 year olds prefer comedy than
drama?
>41
.20
.04
.24
c) How many total people prefer drama?
Total
.6
.4
1
12. The following table shows the population of various towns:
City
Eastville
Northville Southville Westville
Centerville Wayoutville Salemville
Population
30
40
56
48
51
53
64
(thousands)
Suppose that Winstonville with a population of 26,000 is added to the data set. Which of the following is true?
A.
The mean increases
B. The range remains the same
C.
The standard deviation increases
D. The interquartile-range increases
13. A chair lift can hold a maximum of 40,000 pounds and 200 people. A safety inspector is determining if the
chair lift is safe or not. Which measure of central tendency of people’s weight would be most useful to
determine if the chair lift is safe?
A. Mean
B. Median
C. Mode
D. Standard Deviation
14. The number of points scored by a football team in the first ten games of a season are: 10, 14, 17, 20, 35, 35,
38, 42. What would happen to the data distribution if the team scored 27, 27, and 28 in the next three
games?
A. The standard deviation would increase
B. The data distribution would become more peaked and more widely spread.
C. The data distribution would become less peaked and less widely spread.
D. The data distribution would become more peaked and less widely spread.
15. Which of the following is most likely to have the highest standard deviation? To have the lowest
interquartile-range?
A. The average age of 100 people surveyed at the mall
B. The average age of 100 people living in a retirement center
C. The weight of 100 new-born babies.
D. The amount of TV’s that 100 households have.
16. Which of the following statements is true?
A. A data set with high standard deviation means that there is low variability.
B. A data set with low standard deviation means that the data is spread out.
C. As the amount of data increases, the standard deviation usually increases.
D. A data set with many outliers will have a high standard deviation.
17. The math club has 50 members. Each member was asked if he preferred Algebra or Geometry. The results
are shown in the relative frequency table below: Which is true?
A. Eight more underclassmen prefer Geometry than Algebra.
Geometry Algebra Total
Underclassmen .36
B. Thirty-six students are upperclassmen
.28
.64
C. Fourteen more upperclassmen prefer Algebra than Geometry
Upperclassmen .04
.32
.36
D. 32% of the students preferred Algebra.
Total
.4
.6
1.00
18. Listed below is a box plot that shows the scores of two football teams (Team A and B).
a) Which team usually
Team A
scored the most points?
b) Which team has a
higher standard
deviation?
Team B
c) Which team was more
consistent with their
scoring?
d) How much larger is the range of team B than of team A?
19. Circle the graph with the lowest standard deviation. Put a box around the one that has the highest variability.
Graph #1
Graph #2
Graph #3
20. Which of the following examples are most likely to have the largest interval ranges for a histogram and
interquartile range for a boxplot? Which is most likely to have smallest intervals and interquartile range?
I: The weight (in pounds) of 30 people at the mall
II. The ages of 30 people at the mall
III. The amount of money in the wallet of 30 people at the mall.
IV. The shoe sizes of 30 people at the mall.
21. The following are attendance for home football games: 287, 263, 286, 286, 256, 70, 255, and 300. If
the attendance for the 6th game (70) wasn’t included then which measure would increase the most: mean, mode,
median, or standard deviation? Explain your reasoning.
22. Rank the following from having the most likely lowest standard deviation to the most likely highest
standard deviation. Explain your answers:
A: Finding the age (in years) of 50 dogs in the dog pound
B: Finding the age of 20 dogs in the dog pound
C: Randomly selecting 50 numbers from 1-1000
D: Randomly selecting 20 numbers from 1-1000
E: Randomly selecting 50 even numbers from 1-2000