p.9
Measures of Center: Mean and Median
How do the mean and median relate in a roughly symmetric distribution?
They are close together; if the distribution is exactly symmetric, they are the same.
p.14
Five-Number Summary and Boxplots
What are the five-number summary values for the given data?
Min: 16, Q1: 25.5, Median: 34, Q3: 45, Max: 73.
p.21
Organizing a Statistics Problem
What is the first step in organizing a statistics problem?
State the question that you’re trying to answer.
p.21
Organizing a Statistics Problem
What should you do in the 'Do' step of the four-step process?
Make graphs and carry out needed calculations.
p.1
Differences Between Histograms and Bar Graphs
What is the main difference between histograms and bar graphs?
Histograms display the distribution of a quantitative variable, while bar graphs display the distribution of a categorical variable.
p.9
Measures of Center: Mean and Median
In a skewed distribution, where is the mean typically located in relation to the median?
The mean is usually farther out in the long tail than the median.
p.19
Measures of Center: Mean and Median
What is the purpose of using technology in calculating numerical summaries?
To free up time for choosing the right methods and interpreting results.
p.8
Understanding Distribution Patterns: Shape, Center, and Spread
Why is the mean travel time higher than the median in North Carolina?
Because the distribution is right-skewed, pulling the mean toward the right tail.
p.1
Constructing and Interpreting Histograms
How should the horizontal axis be marked in a histogram?
In the units of measurement for the quantitative variable.
p.11
Understanding Distribution Patterns: Shape, Center, and Spread
What are quartiles and the interquartile range resistant to?
They are not affected by a few extreme observations.
p.2
Choosing Appropriate Graphs for Data Types
What is a common mistake when interpreting graphs?
Just because a graph looks nice doesn’t make it a meaningful display of data.
p.1
Choosing Appropriate Graphs for Data Types
What is the correct way to draw bars in a bar graph?
With blank space between the bars to separate the items being compared.
p.8
Measures of Center: Mean and Median
How do you find the median when the number of observations (n) is even?
Average the two center observations in the ordered list.
p.3
Constructing and Interpreting Histograms
What does a dotplot display?
Individual values on a number line.
p.2
Choosing Appropriate Graphs for Data Types
What issue is present in the histograms shown in Figure 1.18(a)?
It compares frequencies from samples of different sizes (100 and 400).
p.5
Measures of Center: Mean and Median
How is the mean (x̄) calculated?
Add the values of observations and divide by the number of observations.
p.15
Constructing and Interpreting Histograms
How many boxplots can the TI-83/84 and TI-89 calculators plot simultaneously?
Up to three boxplots in the same viewing window.
p.1
Understanding Distribution Patterns: Shape, Center, and Spread
What common belief exists about the distribution of IQ scores?
Many people believe it follows a 'bell curve'.
p.17
Calculating and Interpreting Standard Deviation
What does the standard deviation measure?
The typical distance of the values in a distribution from the mean.
p.16
Measures of Center: Mean and Median
What is the most common numerical description of a distribution?
The combination of the mean to measure center and the standard deviation to measure spread.
p.1
Using Percentages for Comparison in Histograms
What should be used on the vertical axis when comparing distributions with different numbers of observations?
Percents instead of counts.
p.8
Choosing Appropriate Graphs for Data Types
What is the significance of the stemplot in the New York travel times example?
It visually represents the data and helps in finding the median.
p.16
Calculating and Interpreting Standard Deviation
What do the standard deviation and variance measure?
They measure spread by looking at how far the observations are from their mean.
p.12
Identifying Outliers in Data Sets
What are the quartile values used in the example for North Carolina workers?
Q1 = 10 minutes, Q3 = 30 minutes.
p.19
Calculating and Interpreting Standard Deviation
How do you specify L1 as the List for calculations on the TI-83/84?
Press 2nd 1 (L1) and then ENTER.
p.17
Calculating and Interpreting Standard Deviation
What is the formula for variance?
s²ₓ = (Σ(xᵢ - x̄)²) / (n - 1)
p.8
Measures of Center: Mean and Median
How do you find the median when the number of observations (n) is odd?
Identify the center observation in the ordered list.
p.6
Measures of Center: Mean and Median
What does it mean when we say the mean is not a resistant measure of center?
It cannot resist the influence of extreme observations or outliers.
p.6
Measures of Center: Mean and Median
How is the mean calculated?
By summing all observations and dividing by the number of observations.
p.1
Constructing and Interpreting Histograms
What is the first step in analyzing the IQ scores provided?
Construct a histogram that displays the distribution of IQ scores effectively.
p.9
Measures of Center: Mean and Median
Why is the median often reported for incomes in skewed distributions?
Because it is less affected by extreme values compared to the mean.
p.10
Measures of Center: Mean and Median
What does the range of a data set represent?
The distance between the maximum and minimum values.
p.15
Understanding Distribution Patterns: Shape, Center, and Spread
What should you do to interpret the IQR value in context?
Calculate the IQR and explain its significance regarding the variability of the data.
p.17
Calculating and Interpreting Standard Deviation
What is the relationship between variance and standard deviation?
Standard deviation is the square root of variance.
p.21
Organizing a Statistics Problem
What was the main question the AP Statistics students aimed to answer?
Do males and females at the school differ in their texting habits?
p.15
Understanding Distribution Patterns: Shape, Center, and Spread
What does the IQR indicate about travel times in New York?
Travel times are more variable in New York, as shown by the lengths of the boxes (the IQR) and the range.
p.2
Choosing Appropriate Graphs for Data Types
Why is a bar graph not appropriate for displaying first-name lengths?
Because first-name length is a quantitative variable.
p.10
Five-Number Summary and Boxplots
What is the first step to calculate quartiles?
Arrange the observations in increasing order and locate the median.
p.17
Calculating and Interpreting Standard Deviation
What is the purpose of squaring deviations in statistics?
To prevent positive and negative deviations from canceling each other out.
p.10
Five-Number Summary and Boxplots
How is the first quartile (Q1) determined?
It is the median of the observations to the left of the median in the ordered list.
p.5
Understanding Distribution Patterns: Shape, Center, and Spread
What type of distribution is described in the stemplot of travel times?
Single-peaked and right-skewed.
p.10
Five-Number Summary and Boxplots
What is the third quartile (Q3)?
It is the median of the observations to the right of the median in the ordered list.
p.3
Constructing and Interpreting Histograms
What do histograms plot?
Counts (frequencies) or percents (relative frequencies) of values in equal-width classes.
p.5
Constructing and Interpreting Histograms
What is the purpose of using stemplots in data analysis?
To visually represent the distribution of quantitative data.
p.4
Understanding Distribution Patterns: Shape, Center, and Spread
What is the average travel time for workers in North Carolina according to the data?
The travel times vary, with individual times including 38, 30, 20, 10, 40, 25, 20, 10, 60, 15, 40, 5, 30, 12, 10, and 10 minutes.
p.3
Identifying Outliers in Data Sets
What are outliers?
Observations that lie outside the overall pattern of a distribution.
p.13
Five-Number Summary and Boxplots
How does the five-number summary divide a distribution?
It divides the distribution roughly into quarters, with about 25% of data values in each segment.
p.4
Choosing Appropriate Graphs for Data Types
Is it appropriate to make a pie chart of the Arbitron data? Why or why not?
No, because the data represents percentages of users who love different devices, which is not a part-to-whole relationship suitable for a pie chart.
p.14
Constructing and Interpreting Histograms
What is the significance of the whiskers in a boxplot?
Whiskers extend to the maximum and minimum data values that are not outliers.
p.5
Measures of Center: Mean and Median
What is the most common measure of center in quantitative data?
The mean (ordinary arithmetic average).
p.3
Choosing Appropriate Graphs for Data Types
What types of graphs can be used to show the distribution of a quantitative variable?
Dotplot, stemplot, or histogram.
p.6
Measures of Center: Mean and Median
What does the mean represent in a group of data?
It represents the 'fair share' value if the total were split equally among all observations.
p.21
Understanding Distribution Patterns: Shape, Center, and Spread
What do numerical measures of center and spread fail to describe?
They do not describe the entire shape of a distribution, such as multiple peaks or clusters.
p.11
Understanding Distribution Patterns: Shape, Center, and Spread
What does the IQR represent in the context of travel times?
The range of the middle half of travel times.
p.15
Identifying Outliers in Data Sets
What is the purpose of the 1.5 × IQR rule?
To determine whether there are any outliers in the data.
p.7
Measures of Center: Mean and Median
What property of the mean is investigated in the activity?
The mean acts as a 'balance point' for a distribution.
p.14
Identifying Outliers in Data Sets
What does the absence of outliers indicate in the data set?
There are no values greater than 74.25 or less than -3.75.
p.7
Measures of Center: Mean and Median
How do you calculate the median of a distribution?
Arrange observations in order, and find the center observation or average the two center observations if n is even.
p.20
Using Percentages for Comparison in Histograms
What does Minitab allow users to do with numerical summaries?
Choose which numerical summaries are included in the output.
p.14
Understanding Distribution Patterns: Shape, Center, and Spread
What shape do the travel time distributions for both states exhibit?
Both distributions are right-skewed.
p.13
Five-Number Summary and Boxplots
What does the central box in a boxplot represent?
It is drawn from the first quartile (Q1) to the third quartile (Q3).
p.6
Measures of Center: Mean and Median
What is a major weakness of the mean as a measure of center?
The mean is sensitive to the influence of extreme observations.
p.9
Understanding Distribution Patterns: Shape, Center, and Spread
What type of distributions do many economic variables, such as college tuitions and personal incomes, have?
They are often right-skewed.
p.19
Constructing and Interpreting Histograms
What is the first step to find summary statistics for travel times using a calculator?
Enter the North Carolina data in L1/list1 and the New York data in L2/list2.
p.6
Measures of Center: Mean and Median
What happens to the mean when an extreme value is excluded?
The mean may decrease significantly, as shown by the example with the 60-minute travel time.
p.14
Calculating and Interpreting Standard Deviation
How is the interquartile range (IQR) calculated?
IQR = Q3 - Q1 = 45 - 25.5 = 19.5.
p.3
Understanding Distribution Patterns: Shape, Center, and Spread
What should you look for when examining any graph?
An overall pattern and notable departures from that pattern.
p.20
Choosing Measures of Center and Spread Based on Data Distribution
What are the two descriptions of center and spread mentioned?
The median and IQR, or the mean (x) and standard deviation (sx).
p.10
Five-Number Summary and Boxplots
What does the interquartile range (IQR) measure?
The range of the middle 50% of the data.
p.3
Understanding Distribution Patterns: Shape, Center, and Spread
What are the simple shapes that distributions can have?
Symmetric, skewed to the left, or skewed to the right.
p.4
Measures of Center: Mean and Median
What percent of elite soccer players had arthritis according to the study?
This requires calculating the number of elite players with arthritis divided by the total number of elite players.
p.13
Five-Number Summary and Boxplots
What is the purpose of the five-number summary?
To provide a quick summary of both center and spread of a distribution.
p.15
Identifying Outliers in Data Sets
What is an outlier in the context of travel times for New York?
The maximum travel time of 85 minutes is an outlier for the New York data.
p.12
Identifying Outliers in Data Sets
What is the purpose of the 1.5 × IQR rule?
To identify outliers in a data set.
p.17
Calculating and Interpreting Standard Deviation
Why do statisticians divide by n - 1 instead of n when calculating variance?
The reason is complicated and will be revealed in Chapter 7.
p.2
Using Percentages for Comparison in Histograms
How did the teacher improve the comparison of word lengths in the two samples?
By using relative frequencies in the histograms.
p.5
Identifying Outliers in Data Sets
What may be considered an outlier in the travel time data?
The longest travel time of 60 minutes.
p.15
Five-Number Summary and Boxplots
What is the five-number summary?
A summary that includes the minimum, first quartile, median, third quartile, and maximum of a data set.
p.19
Calculating and Interpreting Standard Deviation
What should be included in the table for deviations from the mean?
Each value's deviation from the mean and its squared deviation from the mean.
p.16
Calculating and Interpreting Standard Deviation
How do you calculate the squared deviations from the mean?
By squaring the deviations (xi - x)².
p.4
Choosing Appropriate Graphs for Data Types
What does the graph from Arbitron indicate about high-tech device usage?
It shows the percentage of users who 'love' using various high-tech devices and services.
p.12
Identifying Outliers in Data Sets
What does the 1.5 × IQR rule suggest about the travel times of 60 and 65 minutes in the New York data?
They are part of the long right tail of the skewed distribution, not outliers.
p.7
Measures of Center: Mean and Median
Why is the mean sometimes called the 'balance point'?
Because it balances the distribution of values around it.
p.13
Identifying Outliers in Data Sets
How are outliers marked in a boxplot?
Outliers are marked with a special symbol such as an asterisk (*).
p.18
Calculating and Interpreting Standard Deviation
What is the minimum value of sₓ?
0, which occurs only when all observations have the same value.
p.21
Understanding Distribution Patterns: Shape, Center, and Spread
What is the best way to understand a distribution?
By using a graph, as it gives the best overall picture.
p.11
Measures of Center: Mean and Median
How is Q1 determined in the example?
It is the median of the 10 observations to the left of the median.
p.3
Constructing and Interpreting Histograms
What are stemplots used for?
To separate each observation into a stem and a one-digit leaf.
p.1
Understanding Distribution Patterns: Shape, Center, and Spread
What should you describe after constructing the histogram of IQ scores?
Whether the distribution is bell-shaped or not.
p.17
Calculating and Interpreting Standard Deviation
How is variance calculated?
By finding the average of the squared deviations.
p.19
Measures of Center: Mean and Median
What is the mean height of the five basketball starters with heights 67, 72, 76, 76, and 84?
The mean is calculated as (67 + 72 + 76 + 76 + 84) / 5 = 75.
p.9
Identifying Outliers in Data Sets
What is the key difference between the mean and median regarding resistance to outliers?
The median is resistant to outliers, while the mean is not.
p.4
Choosing Appropriate Graphs for Data Types
What type of data does the travel time data set represent?
Quantitative data, as it consists of numerical values representing minutes.
p.7
Measures of Center: Mean and Median
What is the definition of the median?
The median is the midpoint of a distribution, where about half the observations are smaller and half are larger.
p.3
Choosing Measures of Center and Spread Based on Data Distribution
What should you compare when comparing distributions of quantitative data?
Shape, center, spread, and possible outliers.
p.3
Using Percentages for Comparison in Histograms
When should you use relative frequency histograms?
When comparing data sets of different sizes.
p.13
Five-Number Summary and Boxplots
What do the whiskers in a boxplot indicate?
They extend from the box to the smallest and largest observations that are not outliers.
p.18
Calculating and Interpreting Standard Deviation
When should you use sₓ instead of s?
When your data set consists of the entire population.
p.15
Constructing and Interpreting Histograms
What is the first step to create parallel boxplots for travel times using a calculator?
Enter the travel time data for North Carolina in L1/list1 and for New York in L2/list2.
p.14
Constructing and Interpreting Histograms
What is the first step in creating a boxplot?
Ordering the data values to find the five-number summary.
p.15
Constructing and Interpreting Histograms
What feature of the calculator is used to display parallel boxplots?
The Zoom feature, specifically selecting ZoomStat.
p.20
Identifying Outliers in Data Sets
Why might Minitab not identify the maximum value of 85 as an outlier?
Because of the slight difference in quartile calculation, it doesn't meet the 1.5 × IQR rule.
p.14
Identifying Outliers in Data Sets
What is the upper cutoff for outliers using the 1.5 × IQR rule?
Q3 + 1.5 × IQR = 45 + 1.5 × 19.5 = 74.25.
p.3
Identifying Outliers in Data Sets
What does SOCS stand for in data analysis?
Shape, center, spread, and outliers.
p.14
Constructing and Interpreting Histograms
What does a boxplot visually represent?
It shows the five-number summary and identifies outliers.
p.7
Measures of Center: Mean and Median
What is a challenge when finding the median for larger sets of data?
Arranging a moderate number of values in order can be tedious.
p.4
Constructing and Interpreting Histograms
What are boxplots used for?
To visually represent the distribution of quantitative data, including measures of center and spread.
p.19
Calculating and Interpreting Standard Deviation
Which command is used on the TI-83/84 to calculate one-variable statistics?
Press STAT, then choose 1-VarStats.
p.20
Five-Number Summary and Boxplots
What discrepancy is noted between the quartile values from Minitab and the earlier values?
Minitab reports Q3 = 43.75 instead of 42.5.
p.21
Organizing a Statistics Problem
What does the 'Plan' step involve in the four-step process?
Deciding how to answer the question and what statistical techniques to use.
p.9
Identifying Outliers in Data Sets
What happens to the mean if an outlier is present in the data?
The mean increases significantly, while the median remains unchanged.
p.10
Measures of Center: Mean and Median
Why is the range considered a simple measure of variability?
Because it only depends on the maximum and minimum values.
p.9
Understanding Distribution Patterns: Shape, Center, and Spread
Why is it important to consider both mean and median when describing data?
Because a measure of center alone can be misleading without understanding the distribution's spread.
p.14
Understanding Distribution Patterns: Shape, Center, and Spread
How do the travel times to work compare between North Carolina and New York?
Travel times are generally longer in New York than in North Carolina.
p.10
Measures of Center: Mean and Median
What is the median in a data set?
The value that lies halfway up the ordered list of observations.
p.4
Measures of Center: Mean and Median
What percent of the study participants were elite soccer players?
To find this, you would need the total number of participants, which is not provided in the text.
p.18
Calculating and Interpreting Standard Deviation
Why is sₓ preferred over variance?
Because sₓ is in the same units as the original observations, while variance is in squared units.
p.5
Measures of Center: Mean and Median
What does the notation ∙ xᵢ represent in the formula for the mean?
It indicates the sum of all observations.
p.20
Choosing Measures of Center and Spread Based on Data Distribution
When are the median and IQR preferred over the mean and standard deviation?
When the distribution is skewed or has strong outliers.
p.13
Five-Number Summary and Boxplots
What does the five-number summary consist of?
The smallest observation, the first quartile (Q1), the median, the third quartile (Q3), and the largest observation.
p.19
Understanding Distribution Patterns: Shape, Center, and Spread
How can you interpret the standard deviation in the context of the basketball team?
It indicates how much the heights of the players deviate from the mean height.
p.21
Organizing a Statistics Problem
What statistical technique did the students plan to use to compare texting habits?
They planned to make parallel boxplots and calculate one-variable statistics.
p.21
Organizing a Statistics Problem
What data did the students collect for their project?
The number of text messages sent and received by a random sample of students over two days.
p.13
Understanding Distribution Patterns: Shape, Center, and Spread
What is the significance of the smallest and largest observations in a distribution?
They provide information about the tails of the distribution that is missing if only the median and quartiles are known.
p.19
Calculating and Interpreting Standard Deviation
What is the significance of calculating variance and standard deviation?
They provide insights into the spread of the data values.
p.17
Calculating and Interpreting Standard Deviation
What does a standard deviation of 2.55 pets indicate?
The typical distance of the values in the data set from the mean is about 2.55 pets.
p.18
Calculating and Interpreting Standard Deviation
What does the symbol sₓ represent?
The standard deviation of a population.
p.18
Calculating and Interpreting Standard Deviation
What are the steps to find the standard deviation of n observations?
1. Find the squared distances from the mean. 2. Average these squared distances by dividing by n - 1. 3. Take the square root of this average.
p.21
Organizing a Statistics Problem
What is the final step in the four-step process?
Conclude by giving your conclusion in the context of the real-world problem.
p.10
Five-Number Summary and Boxplots
How do you find the quartiles in a data set with repeated values?
Write down all observations, arrange them in order, and apply the rules as if they had distinct values.
p.7
Measures of Center: Mean and Median
What happens to the mean when one penny is moved to the 8-inch mark?
The mean changes based on the new distribution of values.
p.12
Identifying Outliers in Data Sets
What should you do when you find outliers in your data?
Try to find an explanation for them.
p.4
Measures of Center: Mean and Median
What is the purpose of calculating measures of center and spread?
To summarize and describe quantitative data effectively.
p.13
Five-Number Summary and Boxplots
What is a boxplot?
A graphical representation that displays the five-number summary of a distribution.
p.18
Identifying Outliers in Data Sets
What effect do outliers have on sₓ?
A few outliers can make sₓ very large, making it sensitive to extreme observations.
p.4
Identifying Outliers in Data Sets
What is the 1.5 × IQR rule used for?
To identify outliers in a data set.
p.18
Understanding Distribution Patterns: Shape, Center, and Spread
How does the spread of observations affect sₓ?
As observations become more spread out, sₓ gets larger.
p.13
Identifying Outliers in Data Sets
What should you do if outliers are real data?
Choose measures of center and spread that are not greatly affected by the outliers.
p.18
Calculating and Interpreting Standard Deviation
What units does sₓ have?
The same units of measurement as the original observations.
