Title: M5.1 Statistics Quiz
Course: Technical Math for Industry > Section: Module 5.1 Statistics-Mean, Median, Mode and Probabilities

Q: Which table accurately represents the data shown in the given pictograph?
A: (a choice with no text)
Feedback: Incorrect. You identified the correct number of symbols, but it looks as though you used the wrong scale. Each clock represents 3 hours, not 2 hours. Multiply the number of symbols in each row by 3.
Feedback: Correct. Each clock represents 3 hours, so: Trey worked hours Callie worked hours Will worked hours
Feedback: Incorrect. You identified the correct number of symbols, but it looks as though you forgot to factor in the scale. Each clock represents 3 hours, so multiply the number of symbols in each row by 3.
Feedback: Incorrect. You correctly identified that Trey worked 21 hours, but then incorrectly found the number of hours for Callie and Will. Each clock stands for 3 hours.

Q: The graph below shows the number of free throws made by five players on a basketball team.

What was the total number of free throws made during Week 2?
- 30 (Incorrect. You may have found the total number of free throws during Week 1 instead of Week 2.)
- 24 (Correct. The middle bar for each player represents Week 2. The number of free throws they made is therefore .)
- 6 (Incorrect. You may have just found the number of free throws for Player 1 on Week 2. However, you need to find the total number of free throws for all five players during Week 2.)
- 23 (Incorrect. You may have found the total number of free throws for Player 2, or the total number of free throws for Week 3, instead of the total number of free throws for all players during Week 2.)
A: 24

Q: The following circle graph shows how Brad spends his time (excluding sleeping) each week outside of school.

Brad spends the same amount of time playing piano as he does doing which other activity or activities?
- playing football and soccer combined (Correct. The piano section is about of the graph. The football and soccer sections combined are also about of the graph.)
- working and playing football combined (Incorrect. These combined sections are close to, but smaller than, the piano section in size. So Brad spends less time on these two activities than on piano.)
- playing video games, reading, and working combined (Incorrect. These combined sections are close to, but larger than, the piano section in size. So Brad spends more time on these three activities than on piano.)
- doing homework (Incorrect. The homework section is close to, but smaller than, the piano section in size. So Brad spends less time on homework than on piano.)
A: playing football and soccer combined

Q: Tara made this line graph to show the grades that she got on all of her quizzes, in the order that she took them.

Which of these statements about this graph is (are) true?

I  Tara's last four quiz scores were the same.

II  Tara's quiz scores have continually improved.

III  Tara has not had a quiz score lower than 60.
- II and III (Incorrect. Although one of these statements is true, the other is not. Check all three statements again. Remember that the height of each point shows the quiz score, as shown on the vertical axis.)
- I and III (Correct. The last four points are at the same height. So those quizzes had the same score. The graph goes up and down, so the quiz scores have not continually improved. The lowest point has a height of 60, so no quiz score was lower than 60. Therefore, I and III are the true statements.)
- III only (Incorrect. Although statement III is true, it is not the only true statement. Check the other two statements. Remember that the height of each point shows the quiz score, as shown on the vertical axis.)
- I only (Incorrect. Although statement I is true, it is not the only true statement. Check the other two statements. Remember that the height of each point shows the quiz score, as shown on the vertical axis.)
A: I and III

Q: The following stem and leaf plot shows the number of students at the local recreational center each day at 4 PM.

Which data set is represented by this plot?
- 5, 22, 22, 24, 24, 27, 43, 52, 53, 61, 62, 62, 62, 93 (Incorrect. It looks as though you reversed the stem and leaf. To find the original set of numbers from which this stem and leaf plot was created, use each stem as a tens digit and each leaf as a ones digit. For example, the smallest number combines 1 and 6 to make 16; the largest combines 7 and 2 to make 72.)
- 0, 2, 2, 2, 2, 2, 4, 5, 5, 6, 6, 6, 6, 9 (Incorrect. It seems that you have written the leaves and ignored the stems. To find the original set of numbers from which this stem and leaf plot was created, combine each stem with each of its leaves. The stem will be the tens digit of the number and the leaf will be the ones digit. The smallest number combines 1 and 6 to make 16; the largest combines 7 and 2 to make 72.)
- 16, 22, 25, 26, 34, 35, 39, 42, 50, 72 (Incorrect. It looks as though you know how to create the data set from the stem and leaf plot, but you left out the repeated values in the data set. For example, the leaf 2 occurs twice for the stem 4. This means that the number 42 occurs twice in the original collection of numbers.)
- 16, 22, 22, 25, 26, 26, 26, 34, 35, 39, 42, 42, 50, 72 (Correct. To find the original set of numbers from which this stem and leaf plot was created, combine each stem with each of its leaves. The stem will be the tens digit of the number and the leaf will be the ones digit. In this case, there are 14 leaves, so there will be 14 numbers. The smallest number combines 1 and 6 to make 16; the largest combines 7 and 2 to make 72.)
A: 16, 22, 22, 25, 26, 26, 26, 34, 35, 39, 42, 42, 50, 72

Q: Norberto received the following scores on his last five spelling tests: 88, 76, 93, 85, and 98. Which of the following statements is true?
- The mean of the set is less than the median. (Incorrect. You may not have arranged the values in order from least to greatest before finding the middle value, or median.)
- The median of the set of scores is 93. (Incorrect. It appears that you just looked at the list as written and picked the number in the middle. To find the median, you must first put the numbers in order from least to greatest.)
- The mode of the set of scores is 88. (Incorrect. You may have misread one of the test scores, or you may have just picked the first number on the list. The mode is the value that occurs the most often. Because all values here occur only once, there is no mode for this set.)
- The mean and median of the set of scores are the same. (Correct. To find the mean, add the scores and divide that sum by 5, the number of scores: To find the median, arrange the values in order from least to greatest and identify the middle value: 76, 85, 88, 93, 98. The median is 88. The mean and median of this data set are the same.)
A: The mean and median of the set of scores are the same.

Q: Which of the statements below is true for the following set of numbers?

42, 20, 36, 51, 60, 28
- The range is 40 and the midrange is 20. (Incorrect. You subtracted the least value from the greatest value and divided by 2 to find the midrange instead of adding the least and greatest values and dividing by 2.)
- The range and the midrange are equal. (Correct. To find the range, subtract the least value from the greatest value: . To find the midrange, add together the least and the greatest values and divide by 2: The range and the midrange are both 40.)
- The range is 14 and the midrange is 35. (Incorrect. You used the first and last numbers as they were listed (42 and 28) to determine the range and midrange, instead of using the least and greatest values.)
- The range is 60 and the midrange is 39. (Incorrect. You may have thought that the range is 60 because 60 is the greatest value, but you must subtract the least value from the greatest value. The number 39 is the median of this collection, not the midrange. To find this, you must add the least and greatest values and then divide by 2.)
A: The range and the midrange are equal.

Q: Which of the following statements about the box-and-whisker plot below is not true?
- The midrange of the data set shown is 85. (Incorrect. The box-and-whisker plot shows the greatest value of the data set to be 145 and the least value to be 25. Add these values together and divide by 2 to find the midrange: . This statement is true.)
- Both 25 and 145 are values in the set of data. (Incorrect. The endpoints of a box-and-whisker plot represent the least and greatest values of the set of data. The whiskers on this plot begin and end at the numbers 25 and 145. Therefore, these are the least and greatest values of the set. So 25 and 145 are in the set. This statement is true.)
- The median of the data set shown is 55. (Incorrect. The line that divides the box of the box-and-whisker plot is located above 55 on the number line. This represents the median of the data set. This statement is true.)
- There are more data points in the upper two quartiles than in the lower two quartiles. (Correct. The numbers in the upper two quartiles are more spread out than in the lower two quartiles. However, the number of data points in each quartile of a box-and-whisker plot is the same. A quartile is one-fourth of the data.)
A: There are more data points in the upper two quartiles than in the lower two quartiles.

Q: Kevin takes a survey of the ages of people in the library at 10 a.m. and at 6 p.m. on a Wednesday.

Kevin wants to give a talk at the library to new drivers on the dangers of texting and driving. Which statement best describes when Kevin should make the talk and why?
- At 6 p.m., because the range of ages for this data set is less than the range of ages for the 10 a.m. data set (Incorrect. It is true that the range of ages for the data set from 6 p.m. is less than the range of ages for the data set from 10 a.m. But this information does not indicate how young or old the people are, or if they are the age of young drivers.)
- At 10 a.m., because the average age of someone in the library at that time is about 30 (Incorrect. You correctly found the mean age of the data set for the 10 a.m time in the library. However, the mean age of the data set for the 6 p.m. time is about 23, so there would probably be newer drivers in the library at this time. Also, the mean or average could be misleading. There could be many people who are old and many who are young, with an average age around 20, for example, without anyone being around the age of 20.)
- At 10 a.m., because there are more people with cars at the library at that time (Incorrect. Kevin's data does not indicate who owns a car, so he could not schedule his presentation on this basis. Also, even if there were more people with cars, there would not necessarily be more young drivers with cars.)
- At 6 p.m., because the median age of the people in the library at that time is 17 (around the age of new drivers) (Correct. The data set for 10 a.m. has 25 numbers and the number in the middle is 33, so this is the median age. Because the data set for 6 p.m. has 27 numbers and the number in the middle is 17, this is the median age. So it is more likely that younger, newer drivers will be at the library at 6 p.m., which makes it a better time for Kevin's presentation.)
A: At 6 p.m., because the median age of the people in the library at that time is 17 (around the age of new drivers)

Q: A pediatrician wants to show the weight of an infant in pounds and ounces for eight doctor's visits during the first year of her life. He wants to be able to show the parents the infant's approximate weight between visits. Which type of graph is the most appropriate?
- line graph (Correct. A line graph shows continuous data, such as the change in weight over time. A line graph showing weight on the y-axis and time along the x-axis would be the most appropriate.)
- stem-and-leaf plot (Incorrect. A stem-and-leaf plot is used to show the spread of data and would not be appropriate for showing a change over time. It is good for looking at data as a whole, not comparing data.)
- bar graph (Incorrect. Although a bar graph could be used to show the data, it would not best show the change in weight over time. The pediatrician could not use a bar graph to show the infant's approximate weight between visits.)
- circle graph (Incorrect. A circle graph is used to compare parts to the whole and would not be appropriate for showing a change over time. In this situation, you have one category (the baby's weight) with changing numbers. You do not have several categories, each with their own number.)
A: line graph

Q: The following graph, made by the manager of Store B, compares the average cost of a new computer at four different electronics stores.

Which statement best describes why this graph could be misleading?
- You cannot tell if the stores all sell the same computers. (Incorrect. This is true, and might be misleading. But even if the stores do sell different computers, the cost is still less at Store B. There is a better reason why this graph is misleading.)
- The graph is missing the scale on the y-axis, making it unclear as to how much higher the average price of a computer is at one store than another. (Correct. Because you are given no information about the vertical scale, it is not clear what the average price of a computer is at any one store. The graph makes it appear that the price of a computer from Store B is much less than a computer from any other store. Without a scale, there is no way to know if the difference is large or small.)
- There are only four categories being compared, which is not enough to accurately compare computer prices. (Incorrect. You can compare as few as two categories in a bar graph, so the number of categories does not make the graph misleading. There might be other stores that have lower prices than Store B, but Store B does have lower prices than those at Stores A, C, and D.)
- The color of the bar for Store B is different from the color of the other bars in the graph. (Incorrect. It is true that the bar for Store B is a different color, but this is not the best reason that the graph is misleading. The different color does attract your eye to it, but it doesn't change the fact that Store B has lower prices than those at Stores A, C, and D.)
A: The graph is missing the scale on the y-axis, making it unclear as to how much higher the average price of a computer is at one store than another.

Q: A spinner is divided into five sections, each in a different color, as shown below.

After the spinner is spun, the arrow points to one of the colors. Which statement about possible outcomes is true?
- The probability that the arrow will point to yellow is (Incorrect. You may have thought that the probability would be because there are five sections. This would be the case if the sections were equal in size, but they are not. The probability of pointing to yellow is less than because yellow takes up less than of the circle.)
- The probability that the arrow will point to yellow is 0. (Incorrect. You may have chosen this answer because the yellow section of the spinner is the smallest. However, though the arrow is less likely to point to yellow than any other color, this outcome is still possible, so the probability is greater than 0.)
- The probability that the arrow will point to green is the same as the probability that it will point to yellow. (Incorrect. You may have thought that because there is one section for each color, the probability would be the same for any two colors. This would be the case if the sections were equal in size, but they are not. The probability of the arrow pointing to green is greater than the probability of the arrow pointing to yellow, because the green section is bigger.)
- The probability that the arrow will point to red is more than (Correct. There are five colors on the spinner, and the red section is the largest, so it takes up more than of the circle. You would expect the arrow to point to red more than of the time.)
A: The probability that the arrow will point to red is more than

Q: A spinner is divided into equal parts as shown below.

Find the probability of spinning yellow or blue on this spinner.
A: (a choice with no text)
Feedback: Incorrect. You found the probability of spinning only one of the colors for the event, not the probability of spinning either of the colors. The size of the event space is the total number of ways to get yellow or blue.
Feedback: Incorrect. You may have chosen this answer because you were considering two possible colors out of four. However, the probability is the number of ways to get yellow or blue divided by the total number of possible results on the spinner.
Feedback: Correct. There are 8 equally likely outcomes on the spinner, and the event has 6 outcomes in it: {yellow, yellow, yellow, blue, blue, blue}. The probability is:
Feedback: Incorrect. You may have chosen this answer because you were considering two possible colors and there are 8 sections of the spinner. While 8 is the size of the sample space, the number of outcomes in the event space is not 2. It is the total number of ways to end up with yellow or blue.

Q: The cafeteria creates pre-made boxed lunches with equal numbers of the following items:

- a sandwich made with either white or wheat bread and either roast beef or bologna
- a snack that is either chips, popcorn, or pretzels
- a drink that is either bottled water or juice

If Gretchen randomly chooses one of the boxed lunches, what is the probability that she will get a roast beef sandwich and popcorn in her box?
A: (a choice with no text)
Feedback: Correct. Use the Fundamental Counting Principle, or draw a tree diagram, to find the number of possible lunch combinations. There are two breads, two meats, three snacks, and two drinks, so possible combinations. The event space is {(white, roast beef, popcorn, water), (white, roast beef, popcorn, juice), (wheat, roast beef, popcorn, water), (wheat, roast beef, popcorn, juice)}. The size of the event space is 4, so , or , is the probability of the event occurring.
Feedback: Incorrect. You may have found only half of the possible outcomes for the event space. Make sure to use a tree diagram to find all the possible lunch combinations that include both roast beef and popcorn.
Feedback: Incorrect. You may have miscalculated the size of the sample space, thinking that there were only two kinds of sandwiches. Use the Fundamental Counting Principle, or draw a tree diagram, to find the number of possible lunch combinations. Remember, there are two breads, two meats, three snacks, and two drinks.
Feedback: Incorrect. You may have used the number of different categories (bread, meat, snack, drink) as the size of the sample space and the two desired outcomes (roast beef and popcorn) as the size of the event space. Use the Fundamental Counting Principle or a tree diagram to find the number of possible lunch combinations, and then find all the possible lunch combinations that include both roast beef and popcorn.