Deck 7: Summarizing and Displaying Measurement Data

Question 1

A __________ is a quick and easy way to put a list of numbers into order while getting a picture of their shape.

Answer 1

stemplot

Question 2

For Questions , use the following narrative
Narrative: School costs
Suppose a random sample of liberal arts schools was taken, and the average cost per student was measured for each school.The data are pictured in the histogram below:

{School cost narrative} What is the shape of this data set?

Answer 2

Skewed to the right.Data also has an outlier on the high end.

Question 3

One or two scores that are far removed from the rest of the data are called __________.

Answer 3

outliers

Question 4

For Questions , use the following narrative
Narrative: School costs
Suppose a random sample of liberal arts schools was taken, and the average cost per student was measured for each school.The data are pictured in the histogram below:

{School cost narrative} How many schools were sampled in this study?

Question 5

Which of the following statements is true?

A)If a data set is skewed to the right, that means there is bias in the results; the data are higher than they should be.
B)If a data set is skewed to the right, then the higher values are more spread out than the lower values.
C)If a data set is skewed to the right, then the lower values are more spread out than the higher values.
D)None of the above.

Question 6

For Questions , use the following narrative
Narrative: School costs
Suppose a random sample of liberal arts schools was taken, and the average cost per student was measured for each school.The data are pictured in the histogram below:

{School cost narrative} Two measures of center were calculated for this data set and were found to be $26,668, and $34,832.One of them is the mean, and the other is the median.Which one is which, and how do you know that?

Question 7

Which of the following measures of center is affected by an outlier?

A)Mean
B)Median
C)Mode
D)All of the above

Question 8

Name the four kinds of useful information that you can get about a set of measurement data once it has been organized and summarized.

Question 9

A data set is __________ if the two halves of the data set (when cut down the middle) are mirror images of each other.

Question 10

If the bars of a histogram represent the proportion of the total count that falls into each interval, what must the heights of the bars sum to?

A)The total number of numbers in the data set.
B)One.
C)1 divided by the total number of intervals used in the histogram.
D)Not enough information to tell.

Question 11

The mode is most meaningful for which type of data?

A)Measurement data
B)Categorical data
C)Biased data
D)None of the above

Question 12

The __________ is a measure of center with half of the scores falling at or above it and half of the scores falling at or below it.

Question 13

For Questions , use the following narrative
Narrative: Quiz scores
Bob has taken 6 quizzes so far in his statistics class.Each quiz has a possible of 10 total points.Bob's scores are the following: 10, 8, 9, 7, 2, and 9.
{Quiz scores narrative} Find the three measures of center for Bob's quiz scores.

Question 14

Which of the following pictures of a data set allows you to retrieve the actual data (assuming no digits are dropped)?

A)A histogram
B)A stemplot
C)Both a and b
D)Neither a nor b

Question 15

For Questions , use the following narrative
Narrative: Quiz scores
Bob has taken 6 quizzes so far in his statistics class.Each quiz has a possible of 10 total points.Bob's scores are the following: 10, 8, 9, 7, 2, and 9.
{Quiz scores narrative} Explain how (if) Bob's lowest quiz score affects the mean and the median of this data set.

Question 16

Which of the following statements regarding stemplots is false?

A)A stemplot allows you to retrieve the original data (assuming no digits are dropped).
B)A stemplot can never reuse the same stem digit twice.
C)If a certain value in your data set is repeated three times, it must appear 3 times in appropriate stem and leaf of the stemplot.
D)None of the above statements are false.

Question 17

What is the simplest measure of variability in a data set?

A)The interquartile spread
B)The outliers
C)The range
D)The standard deviation

Question 18

The amount of spread in the data is a measure of what characteristic of a data set?

A)Center
B)Variability
C)Shape
D)None of the above

Question 19

Name two questions that can be answered by determining the shape of a data set.

Question 20

For Questions , use the following narrative
Narrative: School costs
Suppose a random sample of liberal arts schools was taken, and the average cost per student was measured for each school.The data are pictured in the histogram below:

{School cost narrative} Describe the four important characteristics of this data set (for example, the shape) using words that a parent exploring the cost of liberal arts colleges would find useful.

Question 21

How do you calculate the interquartile range for a data set?

A)Take the highest value minus the lowest value and divide it by four.
B)Subtract the value of the lower quartile from the upper quartile.
C)Subtract the value of the upper quartile from the lower quartile.
D)Divide the data set into four equal parts and find the range between each of the resulting quarters.

Question 22

Suppose you look at two boxplots comparing the weights of male cats vs.female cats, and you find that the box for the males is much wider than the box for the females.What does this mean about the data sets?

A)Male cats weigh more than female cats overall.
B)Male cats have more variability in their weights than female cats.
C)Weights of male cats are more skewed than for female cats.
D)None of the above.

Question 23

Which of the following does not require the data to be ordered before you can get the right answer?

A)Mean
B)Median
C)Quartiles
D)Range
E)All of the above require the data to be ordered.

Question 24

For Questions , use the following narrative
Narrative: Acceptance rates
A random sample of 50 colleges and universities in the U.S.was selected, and acceptance rates were recorded for each school (percentage of student applicants who were accepted to the school).The following five-number summary was calculated for this data set: lowest = 17; lower quartile = 25.75; median = 36; upper quartile = 47.75; highest = 67.
{Acceptance rates narrative} Describe the center of this data set in words a prospective student would understand.

Question 25

For Questions , use the following narrative
Narrative: Acceptance rates
A random sample of 50 colleges and universities in the U.S.was selected, and acceptance rates were recorded for each school (percentage of student applicants who were accepted to the school).The following five-number summary was calculated for this data set: lowest = 17; lower quartile = 25.75; median = 36; upper quartile = 47.75; highest = 67.

-{Acceptance rates narrative} Find the range of the acceptance rates and give one possible reason that it is such a high number.

Question 26

Name two uses of a boxplot.

Question 27

Which of the following is not included in the five-number summary?

A)Mean
B)Median
C)Lower quartile
D)Highest number
E)All of the above are included in the five-number summary.

Question 28

For Questions , use the following narrative
Narrative: Liberal arts costs
A random sample of 25 liberal arts colleges in the U.S.was selected, and the average cost per student was recorded for each school.The following five-number summary was calculated for this data set: lowest = $17,554; lower quartile = $23,115; median = $26,668; upper quartile = $45,879; highest = $102,262.
{Liberal arts costs narrative} Using the definition of outlier discussed in your textbook, is there an outlier in this data set? Explain your answer.

Question 29

A(n) __________ is any value that is more than 1.5 times the IQR from the closest end of the box in a boxplot.

Question 30

For Questions , use the following narrative
Narrative: Acceptance rates
A random sample of 50 colleges and universities in the U.S.was selected, and acceptance rates were recorded for each school (percentage of student applicants who were accepted to the school).The following five-number summary was calculated for this data set: lowest = 17; lower quartile = 25.75; median = 36; upper quartile = 47.75; highest = 67.
{Acceptance rates narrative} Describe the shape of this data based on the five-number summary.

Question 31

A five-number summary involves the lower quartile, the upper quartile, the lowest number, the highest number, and the __________.

Question 32

If the width of a box in a boxplot is very large, compared to the rest of the boxplot, what does that mean about the shape of the data set?

A)The data are very spread out in the middle.
B)The data are clumped tightly in the middle.
C)The data are not symmetric.
D)Not enough information to tell.

Question 33

The __________ is the distance between the lower and upper quartiles in a boxplot.

Question 34

What are the five numbers used in a five-number summary?

Question 35

For Questions , use the following narrative
Narrative: Liberal arts costs
A random sample of 25 liberal arts colleges in the U.S.was selected, and the average cost per student was recorded for each school.The following five-number summary was calculated for this data set: lowest = $17,554; lower quartile = $23,115; median = $26,668; upper quartile = $45,879; highest = $102,262.
{Liberal arts costs narrative} Make a boxplot of this data set and use it to discuss the shape of the data.

Question 36

Suppose that in a five-number summary you find that a larger gap exists between the extremes and the quartiles than between the quartiles and the median.What does this mean about the shape of the data set?

A)The data are clumped at the high and low ends.
B)The data are clumped in the middle.
C)The data are not symmetric.
D)Not enough information to tell.

Question 37

The __________ are the medians of the two halves of an ordered data set.

Question 38

Suppose that in a five-number summary you find that a larger gap exists between the third quartile and the highest value than between the lowest value and the first quartile.What does this mean about the shape of the data set?

A)Symmetric
B)Skewed right
C)Skewed left
D)Not enough information to tell.

Question 39

Which of the following can not be obtained from a boxplot?

A)Mean
B)Median
C)IQR
D)Range
E)All of the above can be obtained from a boxplot.

Question 40

Describe which numerical summaries (statistics) of a dataset a boxplot is based upon.

Question 41

Which of the following two data sets has the larger standard deviation: Data Set A= {1, 1, 5, 5} or Data Set B= {1, 3, 3, 5}?

Question 42

If the shape of a data set is __________ then the mean and the median should be about equal.

Question 43

What is wrong with the following statement: "Today's temperature of 101 in Los Angeles was a record high for October, a whopping 17 degrees above normal for this date."

Question 44

Which of the following statements is false?

A)If the standard deviation is positive, the mean must be positive.
B)The standard deviation can be negative.
C)If the mean is large, the standard deviation will be large also.
D)All of the above are false.

Question 45

Because the __________ can be distorted by high outliers, the center of a data set involving incomes or prices is usually summarized using the __________.

Question 46

Explain what is meant by the standard deviation in terms that a non-statistician would understand.

Question 47

Suppose a data set is skewed left.What is the most likely relationship between the mean and the median?

A)The mean is larger than the median.
B)The mean is smaller than the median.
C)The mean and the median are not related to each other at all.
D)The mean and the median are essentially equal.

Question 48

Which of the following is not a measure of spread or variability in a data set?

A)Standard deviation
B)IQR
C)Range
D)All of the above are measures of spread or variability in a data set.

Question 49

If you just use an average to describe a set of measurements, is this enough? Explain your answer.

Question 50

Which of the following statements is statistically correct?

A)"Jimmy is taller than normal for a two-year old."
B)"Jimmy is taller than the average two-year old."
C)"Jimmy is taller than the average height of two-year olds."
D)All of the above are statistically correct.

Question 51

For Questions , use the following narrative
Narrative: Create data
Suppose you can create your own data set by choosing from the numbers 1, 2, 3, 4, and 5.You can repeat a number as many times as you wish, as long as your final data set contains four numbers in it.Here are two examples of data sets you could create: {1, 2, 3, 4} or {1, 1, 5, 5}.
{Create data narrative} Create a data set that has the lowest possible standard deviation.

Question 52

For Questions , use the following narrative
Narrative: Create data
Suppose you can create your own data set by choosing from the numbers 1, 2, 3, 4, and 5.You can repeat a number as many times as you wish, as long as your final data set contains four numbers in it.Here are two examples of data sets you could create: {1, 2, 3, 4} or {1, 1, 5, 5}.
{Create data narrative} Create a data set that has mean 3 and standard deviation 0.

Question 53

Which of the following methods is the most appropriate one for 'proving' someone cheated on a multiple choice exam who was allegedly looking at someone else's paper?

A)Examine the two papers and see how many questions they both got wrong, and how many times the same wrong answer was chosen for those questions.
B)Take the student's paper that was allegedly copied from (student X) and compare it to all other students' papers in the class.Take the number of answers that each student matched with student X and make a histogram.Then see where the alleged cheater fell on the resulting histogram.
C)Neither of these methods is appropriate.There is always a chance that two people could have the same answers but no cheating was going on.
D)Both of these methods are equivalent, so either one is appropriate.

Question 54

What is the relationship between the variance and the standard deviation?

A)The variance is the square root of the standard deviation.
B)The variance is the square of the standard deviation.
C)The variance is twice the standard deviation.
D)There is no relationship between them.