Download Math 075 Exam 1 Review (CW and HW) Module 2 Directions: Do not

Math 075
Exam 1 Review (CW and HW)
Module 2
Directions: Do not use minitab. A calculator is allowed. Show work on a separate
sheet of paper. A summary of Mod 2 can be found on my website.
FORMULAS:
∑(𝑥−𝑥̅ )2
SD = √
𝑛−1
IQR = 𝑄3 − 𝑄1
ADM =
You will need to memorize how to get them, I will
provide the formulas for SD and ADM, and you will
need to memorize formula to get IQR
∑|𝑥−𝑥̅ |
𝑛
Remember that ANYTHING we did in class, for homework, or anything in OLI is fair game
for the exam!!! You can use a scientific calculator for the exam, but not your phone and no
sharing calculators.
You need to know how to:



Know the difference between categorical and quantitative variables
How to calculate whether something is an outlier or not
How to calculate the Mean, Median, IQR, ADM, and SD

Analyze changes to center and spread






Find Q1, Q2 (median), Q3, five number summary, and IQR
Construct and analyze boxplots and dotplots
Analyze histograms and boxplots
Compare mean and median (for what graphs will mean be lower/higher than median)
Decide to use mean /SD versus median / IQR and interpret its meaning
Write an essay analyzing/comparing graphs using shape, center, spread and outliers
1. Find the mean and median of the following data set: 2, 4.5, 8, 1, 2, 6.8, 12. Round
answers to the nearest hundredth.
∑|𝑥−𝑥̅ |
2. Find the ADM =
𝑛
of the following data set: 9 , 7 , 11 , 4 , 14 , 2 , 16. Round
answer to the nearest hundredth.
∑(𝑥−𝑥̅ )2
3. Find the SD = √
𝑛−1
of the following set of data: 3, 5, 6, 7, 9, 9, 10. Round
answer to the nearest hundredth.
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4. The following data set shows the quiz raw scores (out of 20 points) for 11 students
in a biology class.
Scores
1
12
14
15
15
16
16
16
17
18
19
a) Find the quartiles Q1 , Q2 (median) and Q3 .
b) Find the Interquartile Range (IQR).
c) Interpret the meaning of the interquartile range in context to this problem.
d) Check the quiz data for outliers. Are there any?
e) Write the five number summary.
e) Create a box plot from the quiz data using the five number summary.
5. For the following set of scores work out the five-number summary and
construct a boxplot. Remember to check for outliers.
4, 2, 3, 7, 13, 4, 5, 6
6. Label each as categorical or quantitative:
a. Temperatures in SCV for the past year____________________________
b. Weather conditions in SCV in past year____________________________
7. What should you be writing about in an essay? What if you’re comparing two
graphs? Make a list of what should be included in the essay paragraph.
12/24/11
Checkpoint Topic 2.1
8. Consider the following histograms and distributions. Choose an appropriate
Question 5
histogram for each of the following distributions.
a. The distribution of length measurements at birth for 10,000 babies?
b. The distribution of quiz scores on an easy quiz?
c. The distribution of annual income for school employees where a high
percentage of employees are entry-level teachers and only a few are
high-paid administrators?
2
Which of the histograms could represent a distribution
for a large random sample of male newborns at a loca
A.
I
B.
II
9. Given the following distribution of the heights of black cherry trees, answer the following:
:questions.
a) What is the x-axis measuring?
b) What is the y-axis measuring?
c) How many cherry trees are measured in this sample?
d) How many trees are less than 70 feet tall?
e) Approximately how many trees are between 65 to 75 feet in
height?
f) How many trees are at least 80 feet tall?
g) What percentage of trees are at least 80 feet tall?
10. Answer the following questions given the distribution of salaries of a random company.
a)
b)
c)
d)
What percentage of employees made a salary of less than $35,000?
What percentage of employees made a salary of more than $80,000?
60% of employees made a salary of less than _______________
How many employees made a salary of less than $35,000?
11) The body temperature of students is taken each time a student goes to the nurse’s
office. The five-number summary for the temperatures (in degrees Fahrenheit) of
students on a particular day is:
One can expect that a typical temperature for a student would fall between ____ and
_____degrees.
3
12) All students in the physical education class completed a basketball free-throw shooting
event and the highest number of shots made was 32. The next day, the PE teacher
realized that he had made a mistake. The best student had actually made 52 shots
(instead of 32). Indicate whether changing the student’s score made each of these
summary statistics increase, decrease, or stay about the same:
a) mean
b) median
c) overall range
d) IQR
13) We collect these data from 50 male students. Which variable is categorical and which
is quantitative?
A) eye color
B) head circumference
C) marital status
D) number of cigarettes smoked daily
E) number of TV sets at home
14) Which one of the quantitative variables in problem 13 is most likely to be symmetric?
Why?
15) Which is true of the data whose distribution is shown?
I. The distribution is skewed to the right.
II. The mean is smaller than the median.
III. We should summarize with mean and standard deviation.
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16) The boxplots show the ages of people involved in accidents according to their role in the
accident.
a) Which role involved the youngest person,
and what is the age?
b) Which role involved the person with the
lowest median age, and what is the age?
c) Which role involved the smallest range
of age, and what is it?
d) Which role involved the largest IQR of
age, and what is it?
e) Which role has the most symmetric
distribution? Explain.
f) Which role has the most skewed
distribution? Explain.
g) 50% of cyclists involved in accidents
were above what age?
h) What percent of pedestrians involved in
accidents were younger than 65 years
old?
17) A class of fourth graders takes a diagnostic reading test, and scores are reported by reading
grade level. The five number summaries for the boys and girls are shown below.
Boys: 2.8 4.1 4.8 5.5 5.6
Girls: 2.1 4.5 4.9 5.6 5.8
a) Which group has the highest score?
Circle one: Boys /
Girls
b) Which group has the greatest range?
Circle one: Boys /
Girls
c) Which group has the highest IQR?
Circle one: Boys /
Girls
d) Draw a boxplot of each using the same sized scale.
e) Which group’s scores appear to be more skewed? Explain.
f) Which group generally did better on the test? Explain.
5
18) The students in a biology class kept a record of the height (in centimeters) of plants
for a class experiment. The following is a list of the data, a histogram, and the descriptive
statistics.
Histogram of height of plants (cm)
5
Frequency
4
3
2
1
0
30
40
50
60
height of plants (cm)
Variable
height of plants (cm)
N
20
Variable
height of plants (cm)
Q3
58.25
N*
Mean
0 51.05
70
StDev
10.63
Minimum
32.00
Q1
43.25
Median
50.50
Maximum
75.00
a) Is it appropriate to use the mean or median to summarize the data? Explain.
b) Describe the distribution of plant heights.
c) When would you use SD instead of IQR?
d) Interpret the meaning of the SD in context for this example.
e) Using the SD, between which two heights was the growth typical?
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19) The 1999 Consumer Reports new Car Buying Guide reported the number of seconds required
for a variety of cars to accelerate form 0 to 30 mph. The cars were also classified into six
categories by type. The following boxplots display the distributions of acceleration times for each
type of car. (Note: the astericks on the boxplot for the small type of cars, these denote outliers.)
a) If we compare a typical car in each category, which type accelerates the fastest? What
part of the boxplots did you compare to make your choice?
b) If we compare the typical range of acceleration times for each car type, which type
performs the most consistently? What part of the boxplots did you compare to make
your choice?
c) Now, let us only focus on the Small cars. If the outliers were removed from the dataset
of Small cars, which of the following measures of spread would be least affected:
Overall range, interquartile range (the distance between the 1st and 3rd quartile marks),
or standard deviation?
20) Review questions from OLI and class work assignments. Review examples of essay
question on the posted summary review notes.
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