Statistics salkind 4e test bank ch04

Chapter 4: A Picture Really Is Worth a Thousand Words Test Bank MULTIPLE CHOICE Which of the following are among the things to remember when creating figures? a Use a lot of text b All graphs communicate several ideas c Do not label anything d Maintain the scale in the graph ANS: D PTS: DIF: Easy REF: Ten Ways to a Great Figure (Eat Less and Exercise More?) OBJ: Using Excel to create charts COG: Knowledge What is the most basic method of illustrating data? a Frequency distribution b Pie chart c Line graph d Polygon ANS: A PTS: DIF: Easy REF: First Things First: Creating a Frequency Distribution OBJ: Creating a histogram and a polygon COG: Knowledge When tallying and representing how often certain scores occur, which type of data illustration method is being utilized? a Class interval b Frequency distribution c Histogram d Polygon ANS: B PTS: DIF: Easy REF: First Things First: Creating a Frequency Distribution OBJ: Creating a histogram and a polygon COG: Knowledge Which of the following is an example of a table? a Frequency distribution b Frequency polygon c Histogram d Line chart ANS: A PTS: DIF: Easy REF: First Things First: Creating a Frequency Distribution OBJ: Creating a histogram and a polygon COG: Knowledge Which of the following is NOT an example of a chart or graph? a Cumulative frequency distribution b Frequency polygon c Variation d Ogive ANS: C PTS: DIF: Medium REF: The Next Step: A Frequency Polygon OBJ: Creating a histogram and a polygon COG: Comprehension Which of the following is NOT an example of a chart or graph? a Frequency polygon b Histogram c Column chart d Class interval ANS: D PTS: DIF: Medium REF: The Next Step: A Frequency Polygon OBJ: Creating a histogram and a polygon COG: Comprehension A good rule of thumb when creating an illustration is a To make sure your graph communicates only one idea b Do not label items c Use a lot of text d Do not worry about centering titles and axis labels ANS: A PTS: DIF: Easy REF: Ten Ways to a Great Figure (Eat Less and Exercise More?) OBJ: Using Excel to create charts COG: Knowledge Which of the following can be used to measure the shape of a distribution? a Mean b Mode c Kurtosis d Median ANS: C PTS: DIF: Medium OBJ: Using the SKEW and KURT functions REF: Kurtosis COG: Knowledge Kurtosis is used to a Measure the central tendency of the distribution b Describe the shape of the distribution c Measure the variance in the distribution d Describe the range of a distribution ANS: B PTS: DIF: Medium OBJ: Using the SKEW and KURT functions REF: Kurtosis COG: Knowledge 10 What you need to calculate first before calculating skewness? a Mean and median b Median and mode c Mode and mean d Mode and variance ANS: A PTS: DIF: Medium OBJ: Using the SKEW and KURT functions REF: Kurtosis COG: Knowledge 11 What you need to calculate first before calculating the kurtosis? a Mean and standard deviation b Median and standard deviation c Mode and variance d Median and variance ANS: A PTS: DIF: Medium OBJ: Using the SKEW and KURT functions REF: Kurtosis COG: Knowledge 12 A distribution of scores in which almost the entire class scored very high but a few students scored fairly low would be _ a Negatively skewed b Positively skewed c Unskewed d Normally distributed ANS: A PTS: DIF: Medium OBJ: Using the SKEW and KURT functions REF: Skewness COG: Application 13 A distribution of scores in which almost the entire class scored very low but a few students scored fairly high would be _ a Positively skewed b Negatively skewed c Unskewed d Normally distributed ANS: A PTS: DIF: Medium OBJ: Using the SKEW and KURT functions REF: Skewness COG: Application 14 What is the term associated with the upper or lower boundary of a set of scores used in the creation of a frequency distribution? a Histogram b Polygon c Class interval d Frequency distribution ANS: C PTS: DIF: Easy REF: First Things First: Creating a Frequency Distribution OBJ: Creating a histogram and a polygon COG: Knowledge 15 If you have a distribution of 50 scores, and you want 10 intervals, what should be the size of your class interval? a 50 b 25 c 10 d ANS: D PTS: DIF: Easy OBJ: Creating a histogram and a polygon REF: The Classiest of Intervals COG: Application 16 If you have a distribution of 100 scores, and you want 20 intervals, what should be the size of your class interval? a 50 b 25 c 10 d ANS: D PTS: DIF: Easy OBJ: Creating a histogram and a polygon REF: The Classiest of Intervals COG: Application 17 If you have a distribution of 20 scores, and you want intervals, what should be the size of your class interval? a 50 b 25 c 10 d ANS: C PTS: DIF: Easy OBJ: Creating a histogram and a polygon REF: The Classiest of Intervals COG: Application 18 If you have a distribution of 50 scores, and you want intervals, what should be the size of your class interval? a 50 b 25 c 10 d ANS: C PTS: DIF: Easy OBJ: Creating a histogram and a polygon REF: The Classiest of Intervals COG: Application 19 Optimally, when choosing a class interval, you should have approximately this many intervals covering the entire range of data: a to 10 b to 10 c 10 to 20 d 20 to 50 ANS: C PTS: DIF: Easy OBJ: Creating a histogram and a polygon REF: The Classiest of Intervals COG: Knowledge 20 Which of the following is the best range of number of data points for a class interval? a 40 b 80 c 20 d ANS: C PTS: DIF: Easy OBJ: Creating a histogram and a polygon REF: The Classiest of Intervals COG: Application 21 The largest class interval goes here on a frequency distribution: a The top b The bottom c In the middle d Either at the top or bottom ANS: A PTS: DIF: Easy REF: First Things First: Creating a Frequency Distribution OBJ: Creating a histogram and a polygon COG: Comprehension 22 What type of chart or graph displays class intervals along an x-axis? a Pie chart b Line graph c Histogram d Tally marks ANS: C PTS: DIF: Easy REF: The Plot Thickens: Creating a Histogram OBJ: Creating a histogram and a polygon COG: Knowledge 23 What is a method of tallying and representing how often certain scores occur? a Histogram b Midpoint c Frequency distribution d Bar chart ANS: C PTS: DIF: Easy REF: First Things First: Creating a Frequency Distribution OBJ: Creating a histogram and a polygon COG: Comprehension 24 What is a graphical representation of a frequency distribution? a Bar chart b Frequency distribution c Histogram d Cumulative frequency distribution ANS: C PTS: DIF: Easy REF: The Plot Thickens: Creating a Histogram OBJ: Creating a histogram and a polygon COG: Knowledge 25 What is the central point of the class interval called? a Median b Mode c Histogram d Midpoint ANS: D PTS: DIF: Easy REF: The Plot Thickens: Creating a Histogram OBJ: Creating a histogram and a polygon COG: Knowledge 26 This is a type of chart in which categories are organized horizontally on the x-axis, and values are shown vertically on the y-axis a Bar chart b Histogram c Line chart d Column chart ANS: D PTS: OBJ: Using Excel to create charts DIF: Easy REF: Excel-lent Charts COG: Comprehension 27 Which of the following NOT have to be filled to create a histogram in Excel? a b c d Input range Output range Medium range Bin range ANS: C PTS: DIF: Medium REF: Using the Amazing Data Analysis Tools to Create a Histogram OBJ: Using Excel to create charts COG: Comprehension 28 A chart that contains a continuous line that represents the frequencies of scores within a class interval is also known as a _ a Standard deviation b Histogram c Frequency polygon d Frequency distribution ANS: C PTS: DIF: Medium REF: The Next Step: A Frequency Polygon OBJ: Different types of charts and their uses COG: Knowledge 29 What is the frequency distribution that shows frequencies for class intervals, along with the cumulative frequency for each? a Frequency distribution b Frequency polygon c Cumulative frequency distribution d Midpoint ANS: C PTS: DIF: Medium OBJ: Different types of charts and their uses REF: Cumulating Frequencies COG: Knowledge 30 This is another word for the lopsidedness of a distribution: a Kurtosis b Skewness c Platykurtic d Leptokurtic ANS: B PTS: DIF: Easy OBJ: Using the SKEW and KURT functions REF: Skewness COG: Knowledge 31 If you wanted to look at the flatness or peak of a distribution, you would need to look at _ a Kurtosis b Skewness c Standard deviation d Standard error ANS: A PTS: DIF: Medium OBJ: Using the SKEW and KURT functions 32 What is another name for a cumulative frequency polygon? a Ogive b Cumulative polygon c Olive REF: Kurtosis COG: Application d Cumulative tally ANS: A PTS: DIF: Medium OBJ: Different types of charts and their uses REF: Cumulating Frequencies COG: Knowledge 33 What is the term associated with the lack of symmetry in a distribution? a Ogive b Skewness c Kurtosis d Variability ANS: B PTS: DIF: Medium OBJ: Using the SKEW and KURT functions REF: Skewness COG: Knowledge 34 In order to say that a distribution is positively skewed, which of the following must be true? a Right tail must be longer than left b Right tail must be shorter than left c Right and left tail must be equal d Curve must be bell shaped ANS: A PTS: DIF: Medium OBJ: Using the SKEW and KURT functions REF: Skewness COG: Knowledge 35 In order to say that a distribution is negatively skewed, which of the following must be true? a Right tail must be longer than the left b Left tail must be longer than the right c Both tails must be of equal length d The curve must be bell shaped ANS: B PTS: DIF: Medium OBJ: Using the SKEW and KURT functions REF: Skewness COG: Knowledge 36 When the left tail of a distribution’s curve is longer the right, what is this called? a Platykurtic b Leptokurtic c Positive skew d Negative skew ANS: D PTS: DIF: Medium OBJ: Using the SKEW and KURT functions REF: Skewness COG: Knowledge 37 When most people scored high on a test of knitting knowledge, and very few people scored low, what is the distribution called? a Platykurtic b Leptokurtic c Positively skewed d Negatively skewed ANS: C PTS: DIF: Medium OBJ: Using the SKEW and KURT functions REF: Skewness COG: Application 38 What is the term associated with how flat or peaked a distribution appears? a Ogive b Skewness c Kurtosis d Variability ANS: C PTS: DIF: Easy OBJ: Using the SKEW and KURT functions REF: Kurtosis COG: Knowledge 39 Which of the following refers to a distribution’s curve that is relatively peaked in comparison to a normal curve? a Platykurtic b Leptokurtic c Positive skew d Negative skew ANS: B PTS: DIF: Medium OBJ: Using the SKEW and KURT functions REF: Kurtosis COG: Knowledge 40 Which of the following refers to distribution’s curve that is relatively flat in comparison to a normal curve? a Platykurtic b Leptokurtic c Positive skew d Negative skew ANS: A PTS: DIF: Medium OBJ: Using the SKEW and KURT functions REF: Kurtosis COG: Knowledge 41 If the mean of a set of scores is greater than the median, what can be said about the distribution? a Negatively skewed b Positively skewed c Leptokurtic d Platykurtic ANS: B PTS: DIF: Medium OBJ: Using the SKEW and KURT functions REF: Skewness COG: Knowledge 42 If the median of a set of scores is greater than the mean, what can be said about the distribution? a Negatively skewed b Positively skewed c Platykurtic d Leptokurtic ANS: A PTS: DIF: Medium OBJ: Using the SKEW and KURT functions REF: Skewness COG: Knowledge 43 If you wanted to examine the proportion of students in this class who are male compared to female, which of the following might you use? a Ogive b Line graph c Pie chart d Frequency polygon ANS: C PTS: DIF: Medium OBJ: Different types of charts and their uses REF: Pie Charts COG: Application 44 If you were interested in tracking your GPA during the time you are in graduate school, which of the following might you use? a Bar chart b Line graph c Pie chart d Histogram ANS: B PTS: DIF: Medium OBJ: Different types of charts and their uses REF: Line Charts COG: Application 45 Which of the following does a histogram most look like? a Pie chart b Bar graph c Frequency polygon d Ogive ANS: B PTS: DIF: Medium REF: Excel-lent Charts Part Deux: Making Charts Pretty OBJ: Different types of charts and their uses COG: Comprehension 46 If you wanted to depict trends in ice cream sales over the four seasons, what kind of chart would you use? a Histogram b Line chart c Pie chart d Bar chart ANS: B PTS: DIF: Medium OBJ: Different types of charts and their uses REF: Line Charts COG: Application 47 What is the horizontal axis on a graph called? a x-axis b y-axis c z-axis d Frequency axis ANS: A PTS: DIF: Easy REF: The Plot Thickens: Creating a Histogram OBJ: Using the Data Analysis tools to create a histogram 48 What is the vertical axis on a graph called? a x-axis b y-axis c z-axis d Nominal axis ANS: B PTS: DIF: Easy REF: The Plot Thickens: Creating a Histogram COG: Comprehension OBJ: Using the Data Analysis tools to create a histogram COG: Comprehension 49 If the mean = 24, and the median = 24, then what can be said of the distribution? a Positively skewed b Negatively skewed c No skew d Leptokurtic ANS: C PTS: DIF: Medium OBJ: Using the SKEW and KURT functions REF: Skewness COG: Application 50 To modify a chart’s elements in Excel, which of the following icons should you click on? a Brush icon b Plus sign icon c Heart shape icon d Minus sign icon ANS: B PTS: REF: Working With Chart Elements COG: Knowledge DIF: Easy OBJ: Using Excel to modify charts 51 If the mean = 34, and the median = 25, then what can be said of the distribution? a Positively skewed b Negatively skewed c Inversely skewed d Symmetrical ANS: A PTS: DIF: Medium OBJ: Using the SKEW and KURT functions REF: Skewness COG: Application 52 If the mean = 12, and the median = 21, then what can be said of the distribution? a Positively skewed b Negatively skewed c Inversely skewed d Symmetrical ANS: B PTS: DIF: Medium OBJ: Using the SKEW and KURT functions REF: Skewness COG: Application TRUE/FALSE A histogram conveys the same information that a frequency polygon does ANS: T PTS: DIF: Easy REF: The Next Step: A Frequency Polygon OBJ: Different types of charts and their uses COG: Knowledge Two sets of scores with different measures of central tendency and variability will result in two different-looking distributions ANS: T PTS: DIF: Medium REF: Fat and Skinny Frequency Distributions OBJ: Using the SKEW and KURT functions COG: Comprehension A visual representation of data can be a much more effective way of illustrating the characteristics of a distribution or data set as compared to numerical values alone ANS: T PTS: DIF: Easy OBJ: Why a picture really is worth a thousand words REF: Why Illustrate Data? COG: Comprehension More is more; the more functions, features, and so forth you can include on a graph, the better ANS: F PTS: DIF: Easy REF: Ten Ways to a Great Figure (Eat Less and Exercise More?) OBJ: Using Excel to create charts COG: Comprehension SHORT ANSWER Why are measures of central tendency and measures of variability important to a visual representation of the distribution of data? ANS: Measures of central tendency indicate the one best score for describing a group of data, whereas measures of variability indicate how diverse, or different, scores are from one another Together, these two measures can result in distributions that look different PTS: DIF: Medium REF: Why Illustrate Data? OBJ: Why a picture really is worth a thousand words COG: Analysis What are some ways to make a good chart? ANS: Minimize chart junk, plan out your chart before making the final copy, say only what you mean to say, label everything, communicate only one idea, keep things balanced, maintain the scale, keep it simple, and limit the number of words PTS: DIF: Medium REF: Ten Ways to a Great Figure (Eat Less and Exercise More?) OBJ: Using Excel to create charts COG: Comprehension What is a frequency distribution? ANS: The most basic way to illustrate data is through the creation of a frequency distribution, which tallies (counts) how often certain scores occur, usually in class intervals PTS: DIF: Medium REF: First Things First: Creating a Frequency Distribution OBJ: Different types of charts and their uses Describe the process of creating a class interval COG: Comprehension ANS: To create a class interval, first select a class interval that has a desired number of data points (e.g., 2, 5, 10, or 20) Next, select how many class intervals you want, so that the entire range of data is covered (e.g., 10, 20, or 50) Then, begin listing the class interval with a multiple of that interval Finally, list the intervals, placing the largest interval at the top of the frequency distribution PTS: DIF: Medium REF: The Classiest of Intervals OBJ: Creating a histogram and a polygon COG: Comprehension What is a histogram? ANS: A histogram is a visual representation of the frequency distribution where the frequencies are represented by bars PTS: DIF: Medium REF: The Plot Thickens: Creating a Histogram OBJ: Creating a histogram and a polygon COG: Comprehension What is a frequency polygon? ANS: A frequency polygon is a continuous line that represents the frequencies of scores within a class interval PTS: DIF: Medium REF: The Next Step: A Frequency Polygon OBJ: Creating a histogram and a polygon COG: Comprehension Besides histograms and polygons, describe four types of charts commonly used in behavioral and social sciences to illustrate data ANS: Four types of charts commonly used in behavioral and social science fields to illustrate data include column charts, bar charts, line charts, and pie charts Column charts are used to show how data change over a period of time or when comparing different categories with one another Bar charts depict the identical information as column charts, but the axes are switched Line charts are used to show a trend in the data at equal intervals Finally, pie charts are used to show proportions of an item that makes up a series of data points PTS: DIF: Medium REF: Other Cool Charts OBJ: Different types of charts and their uses COG: Comprehension What are the four different ways that distributions can be different from one another? ANS: They can differ in their average value, their variability, their skewness, and their kurtosis PTS: DIF: Medium REF: Fat and Skinny Frequency Distributions OBJ: Different types of charts and their uses COG: Comprehension Define skewness ANS: Skewness is a measure of the lack of symmetry in a distribution PTS: DIF: Medium REF: Skewness OBJ: Using the SKEW and KURT functions COG: Knowledge 10 For a normal bell-shaped curve, what is the kurtosis? ANS: The normal bell-shaped curve serves as the reference point for determining kurtosis Because the distribution in question does not differ from the reference distribution, we write that there is no kurtosis PTS: DIF: Medium REF: Kurtosis OBJ: Using the SKEW and KURT functions COG: Analysis 11 Define positive skew and negative skew ANS: Positive skew refers to a distribution where the mean is greater than the median Distributions with positive skew have a long right tail Negative skew refers to a distribution where the median is greater than the mean Distributions with negative skew have a long left tail PTS: DIF: Medium REF: Skewness OBJ: Using the SKEW and KURT functions COG: Comprehension 12 Describe what a leptokurtic distribution looks like and what a platykurtic distribution looks like ANS: A leptokurtic distribution is relatively peaked compared to a normal, bell-shaped curve In these distributions, a high frequency of scores is very close to the mean A platykurtic distribution is relatively flat compared to a normal distribution, reflecting a more equal distribution of scores across the range of scores PTS: DIF: Medium REF: Kurtosis OBJ: Using the SKEW and KURT functions COG: Comprehension 13 Apply the information you have already learned about measures of central tendency—such as the mean, median, and mode—and measures of variability—such as the range, standard deviation, and variance—to the four ways distributions can differ (i.e., average value, variability, skewness, and kurtosis) Imagine you are reviewing the midterm exam grades of students in three different sections of a “Counseling Theories” class Draw yourself pictures of the distributions if that will help you think through the answers You have a figure of the distributions of the most recent exam from those three groups of students As you examine the figure, you realize that the distributions not overlap very much Please label which of the four ways that distributions can differ that is demonstrated by this figure Then, describe what the figure illustrates is different about the mean scores of the midterm exam from the students in the three different sections of the “Counseling Theories” class ANS: The average value or score of the exam grades of the three sections of the class are different This means that the average score for one class section was low, the average score for the second section of the class was in the middle, and the average score of the third section of the class was much better—it was high PTS: DIF: Hard REF: Fat and Skinny Frequency Distributions OBJ: Why a picture really is worth a thousand words COG: Analysis 14 Apply the information you have already learned about measures of central tendency—such as the mean, median, and mode—and measures of variability—such as the range, standard deviation, and variance—to the four ways distributions can differ (i.e., average value, variability, skewness, and kurtosis) Imagine you are reviewing the midterm exam grades of students in three different sections of a “Counseling Theories” class Draw yourself pictures of the distributions if that will help you think through the answers You have a figure of the distributions of the final exam from the three sections of the “Counseling Theories” class While the mean scores among the sections appear to be similar, the distribution of the scores for Section One has a relatively tall peak; the distribution of the scores for Section Two looks normal; and the distribution of scores for Section Three is slightly flat Please label the way that these three distributions differ, and then, describe what might be happening with the means and standard deviations of each section of “Counseling Theories” class ANS: These exam scores differ in variability All the mean scores are the same, but their variability (likely expressed in standard deviation values) is different One section has a small standard deviation, showing more of a peak to the distribution One section has an in-between standard deviation, showing nothing remarkable The final section shows the largest amount of variability, demonstrated by a flatter distribution and a larger standard deviation PTS: DIF: Hard REF: Fat and Skinny Frequency Distributions OBJ: Why a picture really is worth a thousand words COG: Analysis 15 Apply the information you have already learned about measures of central tendency—such as the mean, median, and mode—and measures of variability—such as the range, standard deviation, and variance—to the four ways distributions can differ (i.e., average value, variability, skewness, and kurtosis) Imagine you are reviewing the midterm exam grades of students in three different sections of a “Counseling Theories” class Draw yourself pictures of the distributions if that will help you think through the answers The “Counseling Theories” class had a pop quiz last week, and their quiz scores just came back While the Section One students were taking the quiz, you had to leave the room for an urgent university matter You had your suspicions that the class may have cheated Now that the quiz results are back, you are even more suspicious because the standard deviation of the Section One scores is very small, showing that there is not much variability (dispersion of the scores from the mean) Please label which of the four ways in which this distribution differs Then, give the specific name to this shape of distribution ANS: These exam scores differ in kurtosis The tight standard deviation, or very little spread, would be illustrated by kurtosis—specifically as a leptokurtic distribution PTS: DIF: Hard REF: Fat and Skinny Frequency Distributions OBJ: Why a picture really is worth a thousand words COG: Analysis 16 Apply the information you have already learned about measures of central tendency—such as the mean, median, and mode—and measures of variability—such as the range, standard deviation, and variance—to the four ways distributions can differ (i.e., average value, variability, skewness, and kurtosis) Imagine you are reviewing the midterm exam grades of students in three different sections of a “Counseling Theories” class Draw yourself pictures of the distributions if that will help you think through the answers The Section Two students learned about the cheating that occurred in the “Counseling Theories” Section One class because when you—the faculty member—decided to give them an opportunity to cheat as well, the results of the Section Two class were rather different The results of Section Two indicated that there was not such a small standard deviation this time, and the median was higher than the mean After class, you received an e-mail from a student indicating the advanced notice of the cheating opportunity and that not everyone cheated; some of them kept their integrity and did their work themselves, even if their results would be lower test scores than the others To be more explicit, the mean score of the exam was higher than the previous Section One cheating incident, but there was more of a tail to the left of the distribution Please label which of the fours ways in which this distribution differs from normal Then, give the specific name to this shape of distribution ANS: These exam scores differ in skewness The evidence that the median was higher than the mean and that the tail to the left was longer combine to indicate that there was negative skewness There was a clump of very high pop quiz scores, but there were still some scores that were lower PTS: DIF: Hard REF: Fat and Skinny Frequency Distributions OBJ: Why a picture really is worth a thousand words COG: Analysis ... Using the SKEW and KURT functions REF: Skewness COG: Knowledge 37 When most people scored high on a test of knitting knowledge, and very few people scored low, what is the distribution called? a Platykurtic... of them kept their integrity and did their work themselves, even if their results would be lower test scores than the others To be more explicit, the mean score of the exam was higher than the