Title: Summarizing Data Graphically and Numerically
Course: Question Banks

Q: Consumer Reports analyzed a dataset of 77 breakfast cereals. Here is a part of the dataset.

(Note: Consumer Reports is an non-profit organization that rates products in an effort to help consumers make informed decisions.)

Who are the individuals described by these data?
- Children's breakfast cereals (These data describes breakfast cereals. Children’s cereals are a subset of the data. Target (adult or child) is a categorical variable.)
- Cereal manufacturers (Manufacturer is a categorical variable.)
- Breakfast cereals (these data describe breakfast cereals.)
A: Breakfast cereals

Q: Consumer Reports analyzed a dataset of 77 breakfast cereals. Here is a part of the dataset.

(Note: Consumer Reports is an non-profit organization that rates products in an effort to help consumers make informed decisions.)

Indicate whether the following variable is categorical or quantitative:

Cereal name
- Quantitative (Cereals are the individuals. Cereal name is not a variable.)
- Categorical (Categorical variables have values that are labels. Cereals are the individuals. Cereal name is not a variable.)
- Neither (Cereals are the individuals. Cereal name is not a variable.)
A: Neither

Q: Consumer Reports analyzed a dataset of 77 breakfast cereals. Here is a part of the dataset.

(Note: Consumer Reports is an non-profit organization that rates products in an effort to help consumers make informed decisions.)

Indicate whether the following variable is categorical or quantitative:

Cereal manufacturer
- Quantitative (Quantitative variables have numerical values. Manufacturer is a label.)
- Neither (“Manufacturer” is a variable that labels cereals by name of manufacturer, such as Kellogg or Nabisco.)
- Categorical (Cereals can be labeled or categorized by Manufacturer.)
A: Categorical

Q: Consumer Reports analyzed a dataset of 77 breakfast cereals. Here is a part of the dataset.

(Note: Consumer Reports is an non-profit organization that rates products in an effort to help consumers make informed decisions.)

Indicate whether the following variable is categorical or quantitative:

Target
- Quantitative (Quantitative variables have numerical values. Target audience is a label (adult or child).)
- Neither (“Target” is variable that labels cereals as “adult” or “child”.)
- Categorical (Cereals can be labeled as child or adult.)
A: Categorical

Q: Consumer Reports analyzed a dataset of 77 breakfast cereals. Here is a part of the dataset.

(Note: Consumer Reports is an non-profit organization that rates products in an effort to help consumers make informed decisions.)

Indicate whether the following variable is categorical or quantitative:

Calories
- Categorical (Categorical variables label individuals and put them in categories. The variable “calories” has numerical values.)
- Neither (“Calories” is a variable with numerical values.)
- Quantitative (Quantitative variables have numerical values that can be averaged.)
A: Quantitative

Q: Consumer Reports analyzed a dataset of 77 breakfast cereals. Here is a part of the dataset.

(Note: Consumer Reports is an non-profit organization that rates products in an effort to help consumers make informed decisions.)

Indicate whether the following variable is categorical or quantitative:

Fat
- Categorical (Categorical variables label individuals and put them in categories. The variable “fat” has numerical values, such as 2 grams of fat in a serving.)
- Neither (“Fat” is a variable with numerical values, such as 2 grams of fat in a serving.)
- Quantitative (Quantitative variables have numerical values that can be averaged.)
A: Quantitative

Q: Clinical depression is the most common mental illness in the United States,affecting 19 million adults each year (Source:NIMH,1999). Nearly 50% of individuals who experience a major episode will have a recurrence within 2-3 years. Researchers are interested in comparing therapeutic solutions that could delay or reduce the incidence of recurrence.

In a study conducted by the National Institutes of Health, 109 clinically depressed patients were separated into three groups, and each group was given one of two active drugs (imipramine or lithium) or no drug at all. For each patient, the dataset contains the treatment used, the outcome of the treatment,and several other interesting characteristics.

Below is a summary of the variables in our dataset. Use this to answer the questions below.

- Hospt: The patient's hospital, represented by a code for each of the 5 hospitals 1, 2, 3, 4, 5, or 6
- Treat: The treatment received by the patient (Lithium, Imipramine,or Placebo)
- Outcome: Whether or not a recurrence occurred during the patient's treatment (Recurrence or No Recurrence)
- Time: Either the time in days till the first recurrence, or if a recurrence did not occur, the length in days of the patient's participation in the study.
- AcuteT: The time in days that the patient was depressed prior to the study.
- Age: The age of the patient in years, when the patient entered the study.
- Gender: The patient's gender (1 = Female, 2 = Male)

Examine each of the variables in the dataset as well as their descriptions above.

Which of the following variables is quantitative?
- Hospt (Hospt is not a quantitative variable. Rather, it is a categorical variable, because the numbers represent codes, which are used to identify individual hospitals and place them into categories. As such, the numbers used for the codes (1, 2, 3, 5, or 6) have no arithmetic meaning.)
- Gender (Gender is not a quantitative variable. Rather, it is a categorical variable, because the numbers represent two distinct categories:Female and Male. Thus, the numbers used to represent gender (1=Female and 2=Male) have no arithmetic meaning.)
- Time (Time is a quantitative variable, since it can take on multiple numerical values, which have arithmetic meaning (i.e., it makes sense to add, subtract, multiply, divide, or compare the magnitude of such values).)
A: Time

Q: Clinical depression is the most common mental illness in the United States,affecting 19 million adults each year (Source:NIMH,1999). Nearly 50% of individuals who experience a major episode will have a recurrence within 2-3 years. Researchers are interested in comparing therapeutic solutions that could delay or reduce the incidence of recurrence.

In a study conducted by the National Institutes of Health, 109 clinically depressed patients were separated into three groups, and each group was given one of two active drugs (imipramine or lithium) or no drug at all. For each patient, the dataset contains the treatment used, the outcome of the treatment,and several other interesting characteristics.

Below is a summary of the variables in our dataset. Use this to answer the questions below.

- Hospt: The patient's hospital, represented by a code for each of the 5 hospitals 1, 2, 3, 4, 5, or 6
- Treat: The treatment received by the patient (Lithium, Imipramine,or Placebo)
- Outcome: Whether or not a recurrence occurred during the patient's treatment (Recurrence or No Recurrence)
- Time: Either the time in days till the first recurrence, or if a recurrence did not occur, the length in days of the patient's participation in the study.
- AcuteT: The time in days that the patient was depressed prior to the study.
- Age: The age of the patient in years, when the patient entered the study.
- Gender: The patient's gender (1 = Female, 2 = Male)

Examine each of the variables in the dataset as well as their descriptions above.

Which of the following variables is categorical?
- AcuteT (AcuteT is not a categorical variable; rather, it is a quantitative variable, because it can take on multiple numerical values to represent characteristics of the patient.)
- Time (Time is a quantitative variable, since it can take on multiple numerical values, which have arithmetic meaning (i.e., it makes sense to add, subtract, multiply, divide, or compare the magnitude of such values).)
- Treat (Treat is a categorical variable, because the treatment received by the patients is in the form of categories (Lithium, Imipramine, or Placebo).)
A: Treat

Q: In this study researchers investigated the lifespan of animals living in captivity. They gathered data on 30 different species of animals. Lifespan is the age of the species in years. Researchers want to summarize the distribution of lifespans.

Which graph is best for summarizing the distribution?
- Graph A (This graph is a case-value graph. It does not summarize the lifespan data. For example, it takes some effort to determine how many species live 11 years. We have to trace across the graph and count up the species that fit this description.)
- Graph B (This graph summarizes the lifespan data. For example, it is easy to determine how many species live 11 years.)
A: Graph B

Q: Which of the following distributions will be close to uniform?
- the distribution of heights of 1000 women attending a community college (The distribution of women’s heights will probably be somewhat symmetric with a central peak around the average height.)
- for 1000 community college students the distribution of the number of siblings each student has (This distribution is skewed right, with many students having only a few siblings. Larger numbers of siblings will occur less often in the distribution.)
- roll a die 1000 times and graph the distribution of the numbers on the top face (A die has six-sides. When a die is rolled, all six numbers have an equal chance of appearing on the top face. So the distribution will have roughly the same number of 1’s, 2’s, 3’s, 4’s, 5’s and 6’s. It will be uniform.)
A: roll a die 1000 times and graph the distribution of the numbers on the top face

Q: Which of the following distributions will have a right skew?
- the distribution of birth weights for 1000 babies born at a local hospital (The distribution of birth weights will probably be somewhat symmetric with a central peak around the average weight.)
- the distribution of hourly wages for workers making the federal minimum wage (Workers making the federal minimum wage make the same hourly wage. This distribution will be uniform.)
- the distribution of annual income for entry-level workers at fast food restaurants, along with managers and owners (This distribution is skewed right, with the large number of entry-level workers at the lower end of the income scale. Larger incomes for managers and owners will occur less often in the distribution.)
A: the distribution of annual income for entry-level workers at fast food restaurants, along with managers and owners

Q: Here are data from 507 adults who exercise regularly. The variable is wrist diameter, measured in centimeters. Wrist diameter is the measurement across the top of the wrist between the two prominent parts of the wrist bone.

Determine if the following statement is valid or invalid.

Typical males have a larger wrist diameter than typical females.
- invalid (Look for interval(s) associated with the tallest bars in the histogram. Typical males have wrist measurements between about 11 and 12 cm. Typical females have wrist measurements between about 9.5 and 10.5 cm. Later in the course we will develop more precise ways to identify “typical” measurements.)
- valid (Typical males have wrist measurements between about 11 and 12 cm. Typical females have wrist measurements between about 9.5 and 10.5 cm.)
A: valid

Q: Here are data from 507 adults who exercise regularly. The variable is wrist diameter, measured in centimeters. Wrist diameter is the measurement across the top of the wrist between the two prominent parts of the wrist bone.

Determine if the following statement is valid or invalid.

The overall range in wrist measurements is larger for men.
- valid (A reasonable estimate for the range of male wrist measurements is 4 cm (13.5 – 9.5 = 4). A reasonable estimate for the range of female wrist measurements is 4.5 cm (12.5 – 8 = 4.5).)
- invalid (A reasonable estimate for the range of male wrist measurements is 4 cm (13.5 – 9.5 = 4). A reasonable estimate for the range of female wrist measurements is 4.5 cm (12.5 – 8 = 4.5).)
A: invalid

Q: Here are data from 507 adults who exercise regularly. The variable is wrist diameter, measured in centimeters. Wrist diameter is the measurement across the top of the wrist between the two prominent parts of the wrist bone.

Determine if the following statement is valid or invalid.

A medium male wrist watch fits wrist diameters between 10.5 and 12 centimeters. A medium wrist watch will fit 18% of the males in this sample.
- valid (In the histogram we can see that most men fall within this range, so the percentage should be large. Make sure you are counting all of the men with wrist measurements between 10.5 and 12 cm. There are 45 + 77 + 60 =182 men in this range. This is 74% of the men (182÷247 ≈ 0.737 ≈ 74%).)
- invalid (There are 45 + 77 + 60 = 182 men with wrist measurements between 10.5 and 12 cm. This is 74% of the men (182÷247 = 0.737 ≈ 74%).)
A: invalid

Q: Here are data from 507 adults who exercise regularly. The variable is wrist diameter, measured in centimeters. Wrist diameter is the measurement across the top of the wrist between the two prominent parts of the wrist bone.

Determine if the following statement is valid or invalid.

A medium male wrist watch will fit about 20% of the females in this sample.
- invalid (There are 38 + 10 + 3 = 51 women with wrist measurements between 10.5 and 12 cm. This is 19.6% of the women (51 ÷ 260 ≈ 0.196 ≈ 19.6%). 19.6% is about 20%.)
- valid (There are 38 + 10 + 3 = 51 women with wrist measurements between 10.5 and 12 cm. This is 19.6% of the women (51 ÷ 260 ≈ 0.196 ≈ 19.6%). 19.6% is about 20%.)
A: valid

Q: For the 17 quiz scores graphed in the histogram, estimate the median.
- 13 (The median is the middle score in the ordered list of scores, not the middle of the axis.)
- between 10 and 12 (The median is the middle score in the ordered list of scores. There are 17 scores. So the median will have 8 scores below it and 8 scores above it. There are only 2 scores below 10.)
- between 16 and 18 (There are 17 scores, the median will have 8 scores below it and 8 scores above it. There are 8 scores between 4 and 16. So the median could be 16 or any number between 16 and 18.)
A: between 16 and 18

Q: A college statistics class conducted a survey of how students spend their money. They asked 25 students to estimate how much money they typically spend each week on fast food. They determined that the mean amount spent on fast food each week is $31.52 and the median is $32. Later they realized that a value entered as $2 should have been $20. They recalculate the mean and the median.

Which of the following is true?
- The mean and median will increase. (Only one of these measures of center will increase. Note: since $20 is below the median, it is still in the lower half of the data.)
- The mean will stay the same, but the median will increase. (You have it reversed. Think about how we find the mean and median.)
- Both the mean and median will remain the same. (Only one of these measures of center will remain the same. Note: since $20 is below the median, it is still in the lower half of the data. But we are adding $20 instead of $2 to the overall sum when we calculate the mean.)
- The mean will increase, but the median will remain the same. (The mean increases because we are adding $20 instead of $2 to the overall sum. The median does not change because $20 is still in the lower half of the data. So the position of the middle score remains the same.)
A: The mean will increase, but the median will remain the same.

Q: Which measure of center is the best measure of a typical value for the data set in the histogram above?
- Median (You are correct that the median does a good job here. But the data set is fairly symmetric with no outliers, so the mean will be approximately equal to the median. So the mean also does a good job representing a typical value for this distribution.)
- Mean (You are correct that the mean does a good job here. But the data set is fairly symmetric with no outliers, so the mean will be approximately equal to the median.)
- Both (This data set is fairly symmetric with no outliers, so both measures of center do a good job as a typical measurement for the distribution.)
A: Both

Q: A class of 37 students took a test worth 100 points. The five-number summary of their scores is 55, 67, 73, 81, 98.

The middle 50% of the scores fell between which two values?
- 55 and 98 (The minimum value is 55, and the maximum value is 98, so the interval 55 to 98 captures 100% of the scores (not 50%).)
- 55 and 73 (The minimum is 55, and the median is 73, so the interval 55 to 73 captures the lower 50% of the scores, and not the middle 50% of the scores.)
- 67 and 81 (Q1 = 67 and Q3 = 81. So the middle 50% of the scores fell between these two values.)
A: 67 and 81

Q: A class of 37 students took a test worth 100 points. The five-number summary of their scores is 55, 67, 73, 81, 98.

Identify the false statement:
- At least 25% of the students scored a 67 or below. (This is a true statement. 67 is Q1. 25% of the data is in the first quartile. The phrase “at least” indicates that there may be more than 25% of the scores at 67 or below. If there were many students who scored a 67, the Q1 mark may have scores of 67 above and below it. So it is possible that more than 25% of the scores are a 67 or below.)
- At least 9 students scored between 67 and 73. (This is a true statement. Each quartile contains 25% of the data. 67 is Q1 and 73 is Q2. So 25% of the data occurs between these two scores. The phrase “at least” indicates that there may be more than 25% of the scores in this range. This is possible if many students scored a 67 and/or a 73. In this case the Q1 mark could have scores of 67 above and below it. The same is true for the Q2 mark at 73.)
- At least 25% of the students scored an 81 or above. (This is a true statement: 81 is Q3. 25% of the data is in each quartile. The phrase “at least” indicates that there may be more than 25% of the scores at 81 or above. If there were many students who scored an 81, it is possible that more than 25% of the scores were at or above 81.)
- At least 18 students scored below a 67. (This is a false statement. There are 37 students. Half (18) will have a score below the median. The median is not 67. The median is 73.)
A: At least 18 students scored below a 67.

Q: A survey taken of 140 sports fans asked the question: "What is the most you have ever spent for a ticket to a sporting event?"

The five-number summary for the data collected is:

min = 85, Q1 = 130, Median = 145, Q3 = 150, Max = 250

Should the smallest observation be classified as an outlier?
- No (The IQR is 150 - 130 = 20. Using the 1.5(IQR) criterion we get 130 - 1.5(20) = 100. Since the smallest observation of 85 is smaller than 100, it should be considered an outlier.)
- Yes (The IQR is 150 - 130 = 20. Using the 1.5(IQR) criterion we get 130 - 1.5(20) = 100. Since the smallest observation of 85 is smaller than 100, it should be considered an outlier.)
A: Yes

Q: The boxplot below displays ratings for TV shows during sweeps week:

50% of the shows have a rating greater than:
- 11 (11 is the first quartile (Q1) of the distribution and therefore has 25% of the shows rated below it and 75% of the shows rated above.)
- 15.5 (50% of the shows have a rating greater than the median (M). 15.5 is the middle of the box, halfway between Q1 and Q3, but not the median in this case.)
- 17 (50% of the shows have a rating greater than the median (M). 17 is the middle of the range, halfway between the minimum and the maximum, but not the median in this case.)
- Impossible to tell (50% of the shows have a rating greater than the median (M). Where is the median located according to the boxplot?)
- 14 (50% of the shows have a rating greater than the median (M), which, according to the boxplot, is 14.)
A: 14

Q: The boxplot below displays ratings for TV shows during sweeps week:

What is the percentage of shows that have a rating of less than 20?
- 67% (The boxplot indicates that 20 is the third quartile (Q3) of the rating distribution. What percent of the observations fall below Q3?)
- 84% (The boxplot indicates that 20 is the third quartile (Q3) of the rating distribution. What percent of the observations fall below Q3?)
- 25% (The boxplot indicates that 20 is the third quartile (Q3) of the rating distribution. What percent of the observations fall below Q3?)
- Impossible to tell (The boxplot indicates that 20 is the third quartile (Q3) of the rating distribution. What percent of the observations fall below Q3?)
- 75% (The boxplot indicates that 20 is the third quartile (Q3) of the rating distribution. So by definition, three quarters of the shows (75%) have a rating below it.)
A: 75%

Q: The boxplot below displays ratings for TV shows during sweeps week:

Within which interval of rating would you expect to find the largest number of shows?
- 5-10 (When answering this question, it will be useful to remember that 25% of the data fall below Q1 (11), 25% of the data fall between Q1 (11) and M (14), 25% of the data fall between M (14) and Q3 (20), and 25% of the data fall above Q3 (20). Note that 10 is below the first quartile, so we expect less than 25% of the shows to have a rating in that interval.)
- 15-20 (When answering this question, it will be useful to remember that 25% of the data fall below Q1 (11), 25% of the data fall between Q1 (11) and M (14), 25% of the data fall between M (14) and Q3 (20), and 25% of the data fall above Q3 (20). Note that 15 is above the median, and 20 is Q3, so we expect less than 25% of the shows to have a rating in that interval.)
- 20-25 (When answering this question, it will be useful to remember that 25% of the data fall below Q1 (11), 25% of the data fall between Q1 (11) and M (14), 25% of the data fall between M (14) and Q3 (20), and 25% of the data fall above Q3 (20). Note that 20 is Q3, but 25 is below the largest observation, so we expect less than 25% of the shows to have a rating in that interval.)
- All are equal (Intervals of equal length do not necessarily have the same number of observations fall in them. When answering this question, it will be useful to remember that 25% of the data fall below Q1 (11), 25% of the data fall between Q1 (11) and M (14), 25% of the data fall between M (14) and Q3 (20), and 25% of the data fall above Q3 (20).)
- 10-15 (Note that 10 is below Q1, and 15 is above the M, so we expect more than 25% of the shows to have ratings in that interval. Using a similar reasoning, in all the other intervals we would expect to see less than 25% of the shows.)
A: 10-15

Q: The Web site www.kiplinger.com published "Best Values in Public Colleges," saying they were determined by rankings based on data from more than 500 public 4-year colleges and universities. Using out-of-state rankings that considered the academic quality, total out-of-state costs, and average costs after financial aid, the 50 best-rated colleges were selected. The boxplot pictured displays the average debt per graduate for these colleges.

What percentage of the graduates will have a debt greater than $25,000?
- 19% (The boxplot indicates that $25,000 is the third quartile (Q3). What percentage of the data fall above Q3?)
- 50% (The boxplot indicates that $25,000 is the third quartile (Q3). What percentage of the data fall above Q3?)
- 75% (The boxplot indicates that $25,000 is the third quartile (Q3). What percentage of the data fall above Q3?)
- 81% (The boxplot indicates that $25,000 is the third quartile (Q3). What percentage of the data fall above Q3?)
- 25% (Since $25,000 is the third quartile (Q3), one-quarter of the graduates will have a debt greater than this amount.)
A: 25%

Q: The Web site www.kiplinger.com published "Best Values in Public Colleges," saying they were determined by rankings based on data from more than 500 public 4-year colleges and universities. Using out-of-state rankings that considered the academic quality, total out-of-state costs, and average costs after financial aid, the 50 best-rated colleges were selected. The boxplot pictured displays the average debt per graduate for these colleges.

Of the debts owed, 50% are smaller than what amount?
- $25,000 ($25,000 is the third quartile (Q3) of the distribution. 75% of the debts are smaller than this amount.)
- $22,000 (Although $22,000 is in the middle of the box, halfway between Q1 and Q3, it is not the median.)
- $18,000 ($18,000 is the first quartile (Q1) of the distribution. 25% of the debts are smaller than this amount.)
- $20,600 (50% of the debts are smaller than the median, which according to the boxplot is between 20,000 and 21,000.)
A: $20,600

Q: The Web site www.kiplinger.com published "Best Values in Public Colleges," saying they were determined by rankings based on data from more than 500 public 4-year colleges and universities. Using out-of-state rankings that considered the academic quality, total out-of-state costs, and average costs after financial aid, the 50 best-rated colleges were selected. The boxplot pictured displays the average debt per graduate for these colleges.

Within which interval of debts would you expect to find the largest number of graduates?
- all the intervals are equal (The fact that the four intervals in this problem all represent a difference of $4,000 does not mean they have the same number of observations in them. An interval like 17,000–21,000 has far more observations than the others. This range contains more than one quartile, and the others do not.)
- 25,000–29,000 (All of the values in this interval are above Q3. That means there are less than 25% of the outcomes in this interval. An interval like 17,000–21,000 has far more, since this range contains more than one quartile.)
- 21,000–25,000 (All of the values in this interval are between the median and Q3. That means there are at most 25% of the outcomes in this interval. An interval like 17,000–21,000 has far more, since this range contains more than one quartile.)
- 13,000–17,000 (All of the values in this interval are below Q1. That means there are less than 25% of the outcomes in this interval. An interval like 17,000–21,000 has far more, since this range contains more than one quartile.)
- 17,000–21,000 (Since 17,000 is below the first quartile and 21,000 is above the median, more than 25% of the debts are in this interval.)
A: 17,000–21,000

Q: Three math classes took a quiz, and their scores are displayed in the histograms below.

Which of the three sets has the largest standard deviation? Why?
- Set A, because it has a larger central peak. (The larger central peak means Set A has more values located near its center. This makes its SD smaller than the others.)
- Set B, because it is uniformly distributed. (The uniform distribution in Set B means there are nearly equal counts in each bin. Set B does have a larger SD than Set A, but notice that Set C has more of its values far from its center.)
- The three sets have the same standard deviation because they have equal ranges. (While it is true that the three sets have the same range, that does not mean that they have the same SD.)
- Set C, because it has a larger proportion of its values far away from the center. (Having most of its values far from the mean makes the SD for Set C larger than the rest.)
A: Set C, because it has a larger proportion of its values far away from the center.

Q: Three math classes took a quiz, and their scores are displayed in the histograms below.

Which of the three sets has the smallest standard deviation? Why?
- Set B, because it is uniformly distributed. (The uniform distribution in Set B means there are nearly equal counts in each bin. Set B does have a smaller SD than Set C, but notice that Set A has more of its values near its center.)
- Set C, because of the lack of a large central peak. (The lack of a large central peak means that Set C has most of its values far from the mean. This makes it have a large SD.)
- Set A, because it has most of its values near the center. (The large central peak in Set A means that most of its values are near the mean, so it has a small SD.)
A: Set A, because it has most of its values near the center.

Q: Below are histograms of quiz scores from two other classes.

Which of these two classes have the larger standard deviation? Why?
- Set D, because the central peak is more concentrated. (Generally a concentrated central peak does suggest a smaller SD. However, Set D only appears to have a more concentrated central peak. Pay close attention to the scales.)
- Set E, because its histogram looks bigger. (A histogram looking bigger does not mean it has a larger SD. Pay close attention to the scales in both pictures.)
- The standard deviations of Set D and Set E are equal. The histograms are identical, but displayed on different scales. (Good Job! The two histograms look a bit different, but that is because the horizontal axis in the Set E display goes farther to the right than the Set D display.)
A: The standard deviations of Set D and Set E are equal. The histograms are identical, but displayed on different scales.

Q: Below are histograms of quiz scores from two other classes.

Note: Because all of these sets are approximately symmetric, we know that the mean of each is roughly in the middle of their range.

If everyone in a class scored 100 on a quiz, what is the standard deviation of quiz scores?
- 100 (If everyone scored 100 on a quiz, the mean is 100. What is the SD? (think about the variability))
- It impossible to tell without knowing the mean. (If everyone scored 100 on a quiz, the mean is 100. What is the SD? (think about the variability))
- 0 (If everyone scored 100 on a quiz, there is no variability in the scores. So the SD is 0.)
A: 0

Q: Which measures of center and spread should be used for the data set in the above histogram?
- Mean and SD (This data set is skewed, and has one or more outliers between 16 and 20. Remember, Mean and SD are affected by skew and by outliers.)
- Both give good summaries for this distribution (This data set is skewed, and has one or more outliers between 16 and 20. Remember, Mean and SD are affected by skew and by outliers.)
- Median and IQR (Since the data set is skewed, we should use the median and IQR.)
A: Median and IQR

Q: Which measures of center and spread should be used for the data set in the above histogram?
- Mean and SD (This data set is skewed and the Mean and SD are affected by skew.)
- Both give good summaries for this distribution (This data set is skewed and the Mean and SD are affected by skew.)
- Median and IQR (Since the data set is skewed, we should use the median and IQR.)
A: Median and IQR

Q: Which measures of center and spread should be used for the data set in the above histogram?
- Median and IQR (You are correct that the median and IQR will summarize this distribution well. But the data set is symmetric with no outliers, so the mean and SD will also do a good job representing typical ranges of values for this distribution.)
- Mean and SD (You are correct that the mean and SD will summarize this distribution well. It is symmetric and has no outliers. But the median and IQR will also do a good job representing typical ranges of values for this distribution.)
- Both give good summaries for this distribution (This data set is symmetric with no outliers, so both numerical summaries provide a good summary.)
A: Both give good summaries for this distribution

Q: A classroom of students has their heights measured (in inches) for statistics investigation. The tallest student in the class is 71 inches tall. One student is assigned to record all the values. That student made a mistake when recording one of the values. When they meant to record the 71, they accidentally entered 711.

How will the median and IQR be affected by this mistake?
- The median and IQR will be increased by the mistake. (Remember that the calculation of median and IQR are based on the order of the data. Making the largest number even larger will not affect the order.)
- The median and IQR will be decreased by the mistake. (Remember that the calculation of median and IQR are based on the order of the data. Making the largest number even larger will not affect the order.)
- The median and IQR will be unaffected by the mistake. (The calculation of median and IQR are based on the order of the data. Making the largest number even larger will not affect the order.)
A: The median and IQR will be unaffected by the mistake.

Q: A classroom of students has their heights measured (in inches) for statistics investigation. The tallest student in the class is 71 inches tall. One student is assigned to record all the values. That student made a mistake when recording one of the values. When they meant to record the 71, they accidentally entered 711.

How will the mean and SD be affected by this mistake?
- The mean and SD will be decreased by the mistake. (This mistake made one value larger (increasing the mean) and farther from the rest of the values (increasing the SD).)
- The mean and SD will be unaffected by the mistake. (This mistake made one value larger (increasing the mean) and farther from the rest of the values (increasing the SD).)
- The mean and SD will be increased by the mistake. (Making a value larger will increase the mean. Moving the maximum value farther from the mean will increase the SD.)
A: The mean and SD will be increased by the mistake.