Unit 2 Data Representation and Distributions.docx

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21/26 that's 81% RETAKE 21 questions were answered correctly . 5 questions were answered incorrectly . 1 The first quartile (Q1) value from the above box plot is __________.  29

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 52  33  40 RATIONALE Note the value for Q1 is the left edge of the box, which is 33. CONCEPT Five Number Summary and Boxplots Report an issue with this question 2 The formula for the standard deviation of a sample is: Select the true statement for the following data set that has a mean of 8: 4, 6, 6, 6, 9, 9, 12, 12 Answer choices are rounded to the hundredths place.  The variance is 2.98 and the standard deviation is 8.86.  The variance is 7.50 and the standard deviation is 2.98.  The variance is 8.86 and the standard deviation is 2.98.  The variance is 8.86 and the standard deviation is 7.50. RATIONALE We can first calculate the variance of the data, , by using the part of the formula under the square root:

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Next, we can find the standard deviation, , by simply taking the square root of the variance: We can also use the statistical functions in Excel to quickly find the variance and standard deviation. CONCEPT Standard Deviation Report an issue with this question 3 Sara wonders what percentage of her students answered at least half of the quiz questions incorrectly. The relative cumulative frequency of students who earned a score of 20 or lower on the quiz is __________ .  28%  14%  68%  34% RATIONALE To get the relative frequency of 20 or lower, we need to find the cumulative number of 20 or less. We simply add up any bin that has the number 20 or less, such as the bin that shows scores of 1-5, 6-10, 11-15, and 16-20. This would be: To get relative frequency, we will take this cumulative number and

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divide it by the total number of students. CONCEPT Cumulative Frequency Report an issue with this question 4 Consider this histogram showing the number of students in grade five who have one or more pets What is the difference in the number of students with the most and least numbers of pets?  4  10  2  9 RATIONALE The most number of pets is 10 and there is 1 person who has this many pets. The least number of pets is 1 and there are 5 people with 1 pet. So the difference in the number of people would be: CONCEPT Histograms Report an issue with this question 5 A data set has its first and third quartiles as 9 and 17, respectively. Which of the following data points would be considered an outlier for the data set?  27

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 17  3  41 RATIONALE To find an outlier we note the lower bound and upper bound for outliers are: First, find the interquartile range: Next, plug this value in for IQR, along with Q1 and Q3 to find the lower and upper bounds. Anything lower than -3 and larger than 29 will be an outlier. 41 is outside of these bounds and is an outlier. CONCEPT Outliers and Modified Boxplots Report an issue with this question 6 Tomijia and her nine classmates took a standardized test. Their scores were: 42, 44, 56, 71, 74, 83, 89, 90, 90, 92 If Tomijia received an 89 on the test, which percentile is she in?  The 90th  The 80th  The 70th  The 60th

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RATIONALE 89 is the 7th largest value out of a total of 10 values. We can find this percentile with the following calculation: This tells us that 89 is in the 70th percentile. CONCEPT Percentiles Report an issue with this question 7 Nick just received his test back. He scored a 24 out of a possible 60 points. His teacher told him the mean score on the test was a 35, with a standard deviation of 6. What is Nick's z-score?  1.83  4.17  -1.83  -4.17 RATIONALE Recall that the z-score can be calculated with the following formula: The given value is 24 points, the mean is 35 points, and the standard deviation is 6 points. Plug these values in to get the following z-score: This also tells us that a score of 24 points is 1.83 z-scores or standard deviations below the mean. CONCEPT Standard Scores and Z-Scores

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Report an issue with this question 8 For a class reading competition, the students were asked to read a book. Mike, Jack, and Rayon discussed the number of pages they read on the first day. Jack made a graph to represent the data. Which statement explains why the graph is misleading?  The vertical axis should be in terms of hours read instead of number of pages read.  The scale of intervals on the horizontal axis is inconsistent.  The vertical scale made Jack's bar look twice the size of Mike's bar.  The horizontal axis should be in terms of minutes instead of names. RATIONALE Due to the graph starting at 50 and not 0, it makes the number of pages read by Jack look twice as many as Mike read. Jack read 75 pages, while Make read 62.5 pages. So it is only 1.2 times as large, not double. CONCEPT Misleading Graphical Displays Report an issue with this question 9 In which of these cases should the mean be used?  When the data is right-skewed  When the data is left-skewed  When the data is symmetric  When the data has extreme values RATIONALE

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Since the mean uses the actual values in the data, it is most affected by outliers and skewness. So, we only want to use the mean when the data is symmetric as a measure of centrality. When the data is skewed, the median is a better measure. CONCEPT Measures of Center Report an issue with this question 10 When a survey was conducted among 100 students to find their favorite pizza topping, 45 students voted for pepperoni, 25 for mushrooms, and 30 voted for cheese. If a pie chart were made showing the number of votes for each topping, the central angle for the cheese sector would be __________.  162°  198°  90°  108° RATIONALE Recall that to get the angle for something in a pie chart we use the following formula: So in this case, the central angle for the cheese sector would be: CONCEPT Bar Graphs and Pie Charts Report an issue with this question 11 A class of 20 students have one week to complete a math assignment of 30 questions. At the end of the first day, the students had completed the following number of questions:

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5, 7, 4, 6, 1, 8, 9, 4, 4, 5, 10, 4, 6, 5, 3, 6, 5, 6, 0, 2 How many modes are in the given data set?  2  5  4  3 RATIONALE The mode is the most frequently occurring value. In this dataset 4, 5, and 6 each occur 4 times. So there are three modes or we say the dataset is trimodal. CONCEPT Mean, Median, and Mode Report an issue with this question 12 Which of the following statements about a negatively skewed distribution is true?  The distribution of the data tails to the right of the median.  The distribution of the data tails to the left of the median.  The distribution of the data features two modes.  The mean and median have the same value. RATIONALE Skewness refers to how the data trends to the left or right. If a dataset is skewed, it is not symmetric. The direction of the tail of a distribution tells you which direction the skew lies. If there is negative skew, this implies the skew is to the left. If the distribution trends to the left, it will have a mean that is smaller than the median due to those lower values.

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CONCEPT Shapes of Distribution Report an issue with this question 13 Let x stand for the number of minutes spent waiting in line for a rollercoaster at an amusement park. 81 people are sampled at a time. The sample mean is 18 minutes and the sample standard deviation is 0.5 minutes. What is the standard deviation of the population?  0.5  4.5  18  2 RATIONALE The standard deviation of the sampling distribution, , is equal to the standard deviation of the original population, , divided by the square root of the sample size, . We know the sample standard deviation is 0.5 and the size of the sample is 81, so we can solve for the standard deviation of the population: CONCEPT Center and Variation of a Sampling Distribution Report an issue with this question 14 The graph in the figure shows the change in the Consumer Price Index over an 11-year period.

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Which segment of the graph indicates no change in the Consumer Price Index?  H  A  E  D RATIONALE In this graph, a segment that is horizontal would show no change in the consumer price index. This occurs at segment E. CONCEPT Line Charts and Time-Series Diagrams Report an issue with this question 15 Select the statement that correctly describes a normal distribution.  It is a uniform distribution, as all of the values have equal frequency.  It is a negatively skewed distribution, as the extreme values are less than the median.  It is a positively skewed distribution, as the extreme values are greater than the median.  It is a symmetric distribution, as the mean and the median are the same. RATIONALE A normal distribution is a bell-shaped and symmetric distribution. So it has a smooth peak, which tells us the mean and median are the same. CONCEPT Normal Distribution Report an issue with this question 16

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The dot plot below shows the height (in cm) of students in a class How many students are taller than 140 centimeters?  10  12  11  8 RATIONALE If we sum up the X's that represent a student who is taller than 140 centimeters, we need to include the number of students who are 141 cm tall, 142 cm tall, 143 cm tall, etc. This looks like: So 10 students are taller than 140 centimeters. CONCEPT Dot Plots Report an issue with this question 17 Select the statement that is TRUE.  The interquartile range (IQR) covers the middle 50% of a data set.  The interquartile range (IQR) is the middle value of a data set.  The interquartile range (IQR) is the average value of a data set.  The interquartile range (IQR) is influenced by outliers. RATIONALE Recall that the interquartile range is the difference of Q3 and Q1, or in other words, from the 75th percentile to the 25th percentile.

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So the IQR is the middle 50% of the data from the 25th to the 75th percentile. CONCEPT Range and Interquartile Range (IQR) Report an issue with this question 18 The quality control inspector of a factory manufacturing screws found that the samples of screws are normally distributed with a mean length of 5.5 cm and a standard deviation of 0.1 cm. If the distribution is normal, what percent of data lies between 5.3 centimeters and 5.7 centimeters?  68%  34%  95%  99.7% RATIONALE Recall that if the data is normal, then the 68-95-99.7 rule applies which states that 68% of all data points fall within one standard deviation of the mean, 95% of all data points fall within two standard deviations of the mean, and 99.7% of all data points fall within three standard deviations of the mean. 5.3 cm and 5.7 cm are both 0.2 cm from the mean of 5.5 cm, which is the same as two standard deviations (0.1cm * 2) in either direction. This tells us that 95% of the data should lie between 5.3 cm to 5.7 cm. CONCEPT 68-95-99.7 Rule Report an issue with this question 19

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A fast-food restaurant gave a “Customer Satisfaction Survey” in which 1500 customers rated how satisfied they were with service. The results are shown below as a table. Rating Frequen Extremely Satisfied 234 Satisfied 443 Neutral 246 Dissatisfied 203 Extremely Dissatisfied 374 The relative frequency of people who were extremely dissatisfied with the service is __________.  24.9%  29.5%  38.5%  20.3% RATIONALE To get the relative frequency, we take the frequency of the value and divide it by the total number. So in this case for extremely dissatisfied, the relative frequency would be: CONCEPT Frequency Tables Report an issue with this question 20 Which of the following statements is true?  A standard normal curve has a mean of 0 and a standard deviation of 2.  A standard normal curve has a mean of 1 and a standard deviation of 2.

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 A standard normal curve has a mean of 0 and a standard deviation of 1.  A standard normal curve has a mean of 1 and a standard deviation of 1. RATIONALE The standard normal distribution is a normal distribution that is centered at 0 and a standard deviation of 1. CONCEPT Standard Normal Distribution Report an issue with this question 21 Which of the following statements is true?  The Central Limit Theorem is applicable only for data sets comprising thirty or more samples.  The Central Limit Theorem is applicable only for data sets comprising more than thirty samples.  The Central Limit Theorem is applicable only for data sets comprising exactly thirty samples.  The Central Limit Theorem is applicable only for data sets comprising less than thirty samples. RATIONALE Recall that the Central Limit Theorem outlines that when the sample size is large, then the distribution of sample means will be approximately normal. For most distributions, the sample size is n ≥ 30, meaning a sample of 30 or more observations is considered a good sample size. CONCEPT Shape of a Sampling Distribution Report an issue with this question 22

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Consider the times (in seconds) that it took children and adults to solve a Rubik’s cube at a competition. What does the circled section represent?  One child solved the Rubik's cube in 21.7 seconds.  21 children completed the Rubik's cube in 7 minutes.  21 children completed the Rubik's cube in 7 seconds.  One child took 72 seconds to solve the Rubik's cube, while another took 71 seconds to solve it. RATIONALE If we recall that the stem and leaf can give us the actual values in the dataset, then the circle corresponds to 71 and 72. We can then note that there are 2 children who solved the Rubik's cube at 71 and 72 seconds. CONCEPT Stem-and-Leaf Plots Report an issue with this question 23 At Brent's school, the final grade for his U.S. History course is weighted as follows:  Tests: 30%  Quizzes: 50%  Homework: 20% Brent has an average of 82% on his tests, 94% on his quizzes, and 50% on his homework. What is Brent's weighted average?  69.6%  74.8%

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 75.3%  81.6% RATIONALE In order to get the weighted average we use the following formula: CONCEPT Weighted Mean Report an issue with this question 24 Select the false statement about standard deviation.  It is calculated using the mean.  It is the square root of variance.  It is the average of the squared differences of the values from the mean.  It is a measure of how spread out the values of a data set are. RATIONALE Recall that the standard deviation (SD) is equal to the square root of the variance and the variance is the average of the squared distances from the mean. So, the standard deviation is the average distance to the mean. CONCEPT Standard Deviation Report an issue with this question 25 Ralph records the time it takes for each of his classmates to run around the track one time. As he analyzes the data on the graph, he notices very little variation between his classmates’ times. Which component of data analysis is Ralph observing?

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 The center of the data set  The overall shape of the data  An outlier in the data set  The overall spread of the data RATIONALE Since Ralph is looking at the variation of data, this is examining the spread of the data. CONCEPT Data Analysis Report an issue with this question 26 A baseball scout recorded the type of pitch a pitcher threw during a game and whether it was thrown for a strike or a ball. Which of the following statements about the stack plot is true?  The pitcher's least accurate pitch (lowest percentage of strikes) is the slider.  The pitcher threw the curveball most often.  The pitcher threw the changeup the most often.  The pitcher's least accurate pitch (lowest percentage of strikes) is the curveball. RATIONALE For curveballs, it seems like roughly 50% are thrown for a strike. In the other pitches, the percentage of pitches thrown for strikes all seem to be greater than 50% since the strike area is more than half of the total pitches.

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Unit 2 Data Representation and Distributions

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