Test 1

LAMC
Yun
Math 137 Test 1 Module 1-2
_____
Last name________________________________
10/1/2014
First name__________________________
You may use a calculator but not a cellphone, tablet or an iPod. Please clearly mark your choices
on multiple choice questions and box your answers on free response questions.
1. (10 pts.) Here is a histogram of the Distribution of grades on a quiz.
How many students took the quiz? _____________
What percentage of students scored below a 60 on the quiz? (Assume left-hand endpoints are
included in each bin.)
0.20%
2%
3%
20%
Can we answer to questions below using the histogram? Choose “yes” if the histogram provides
information needed to answer the question.
What is the lowest grade on the quiz?
What percentage of the students scored between 75 and 80?
What percentage of the students made an A on the quiz if an A is 90 or better?
How many students fail the quiz if s score below 70 is considered failing?
What was the most common score on the quiz?
Yes
Yes
Yes
Yes
Yes
No
No
No
No
No
2. (4 pts.) Which of the following distributions will be close to uniform?
the distribution of heights of 1000 women attending a community college
roll a die 1000 times and graph the distribution of the numbers on the top face
for 1000 community college students the distribution of the number of siblings each student
has
3. (4 pts.) Which of the following a distribution will have a right skew?
the distribution of hourly wages for workers making the federal minimum wage
the distribution of birth weights for 1000 babies born at a local hospital
the distribution of annual income for entry-level workers at fast food restaurants, along with
managers and owners
1
4. (6 pts) A researcher conducts an experiment to examine the effect of a new fertilizer on plant
growth. She applies the fertilizer at regular intervals to 68 pepper plants. Another 59 plants
receives just water.
Tell whether the following statement
provides a valid conclusion that can be
drawn from the dotplots:
(a) The fertilizer had inconsistent results. The group treated with fertilizer
had more variability in height than the untreated group.
Valid
Invalid
(b) The fertilizer had inconsistent results. The group treated with fertilizer
had more variability in height than the untreated group.
Valid
Invalid
(c) The fertilizer had a negative effect on the plant height because the
shortest plant is in the fertilizer group.
Valid
Invalid
5.
(6 pts.) The boxplot to the right displays ratings for TV shows during
sweeps week. Answer the following questions.
(a) 50% of the shows have a rating greater than:
14
11
17
15.5
impossible to tell
(b) What is the percentage of Shows that have a rating of less than 20?
84%
25%
67%
75%
impossible to tell
(c) Within which interval of rating would you expect to find the largest number of shows?
5 - 10
10 - 15
15 - 20
20 -25
All are equal
6. (4 pts.) The distribution of the top 1% of individual incomes in the U.S. is strongly skewed to
the right. In 1997, the two measures of center for the top 1% were $330,000 and $675,000.
Which number best represents the mean income and which represents the median income?
$330,000 is both the median and the mean.
$330,000 is the median and $675,000 is the mean.
$330,000 is the mean and $675,000 is the median.
It is impossible to tell from the information given.
2
7. (4 pts.) Which University has a less variability in the ages of their faculty? Pick the statement
that gives the best reason.
University A because the overall range is smaller.
University A because the IQR is smaller.
University B because the standard deviation is smaller.
University B because there is no outlier.
8. (8 pts.) Refer to the histogram to the given. Answer the following questions. Assume that the
histograms are drawn to scale.
(a) Which of the histograms has the largest median?
Histogram I
Histogram II
Histogram III
Histogram IV
(b) Which of the histograms has the largest interquartile range (IQR)?
Histogram I
Histogram II
Histogram III
Histogram IV
(c) Which histogram shows a distribution of exam scores on a difficult exam?
Histogram I
Histogram II
Histogram III
Histogram IV
(d) Which of the histograms has a mean that is larger than the median?
Histogram I
Histogram II
Histogram III
Histogram IV
3
9. (6pts.) Here are the boxplots showing annual incomes (in thousands of dollars) of households
in two cities. Answer the following questions.
(a) Which city has a greater percentage of households
with annual incomes between $50,000 and $80,000?
Statstown
Medianville
Both Cities have about the same percentage
It is impossible to tell from the boxplot
(b) Which city has a greater percentage of households with annual incomes above $80,000?
Statstown
Medianville
Both Cities have about the same percentage
It is impossible to tell from the boxplot
(c) Which city has more households?
Statstown
Medianville
Both Cities have about the same percentage
It is impossible to tell from the boxplot
10. (7pts.) Scores for a quiz given to 15 students are shown in the dotplot. Find the median and
IQR:
4
11. (15pts.) Consider the following data set:
14, 12, 8, 13, 13, 8, 16, 15, 14, 14, 3, 18, 20, 18
(a) Find the Mean (round to one decimal place if needed)
(b) Find the Median
(c) Find the Range
(d) Find the 5 point summary
(e) Find the IQR
(f) Identify any outliers
(g) Create a boxplot
0
5
10
15
5
20
25
12. (8pts.) Calculate the ADM and the standard deviation for the following set of data. Show all
steps and calculations.
7, 12, 4, 6, 20, 8, 13, 24
ADM =_____________
Standard Deviation =____________
13. (6pts.) Consider a quantitative data set with histogram shown below.
(a) Which would be a better tool for measuring center?
Median
IQR
Mean
Standard Deviation
(b) Which would be a better tool for measuring spread?
Median
IQR
Mean
Standard Deviation
6
14. (3pts.) Suppose that 40 students take a quiz and everyone in the class scores an 80. The
standard deviation of scores for this quiz is:
80
2
0
100
15. (3pts.) Which question is best answered by an experiment?
Is there an association between the number of hours college students spend each week on
Facebook and their college GPA?
Do the majority of community college students plan to vote in the next presidential election?
Does use of computer-aided instruction in college math classes improve test scores?
16. (3pts.) When conducting a survey, it is important to use a random sample because random
samples:
help us make cause-and-effect connections
avoid bias and are representative of the population
systematically favor the correct response over every other response on each question
are an example of a census
17. (3pts.) A classroom of students has their height measured (in inches) for statistics
investigation. The tallest student in the class is 71 inches tall. One student is assigned to
record all values. That student made a mistake when recording one of the values. When they
meant to record the 71, they accidentally entered 711. Which measure will be affected greatly?
Mean
Median
IQR
7

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