Title: Unit 8 Quiz
Course: Technical Math for Industry

Q: Christa sells bracelets during the summer months, and she made this pictograph to represent her sales.

How many bracelets did Christa sell in June?
- 12 (Correct. There are three bracelet symbols for June, and each symbol represents four bracelets. Christa sold 12 bracelets.)
- 3 (Incorrect. It appears that you only counted the number of bracelet symbols, ignoring the fact that each symbol stands for four bracelets sold.)
- 7 (Incorrect. You may have made an error when computing, adding 4 and 3 instead of multiplying.)
- 20 (Incorrect. You may have accidentally looked at July instead of June.)
A: 12

Q: The graph below shows the number of inches of rain during the summer months of 2009 and 2010.

How many more inches of rain occurred during the summer of 2010 than during the summer of 2009?
- 2 (Correct. The total rainfall for the summer of 2009 was and the total rainfall for the summer of 2010 was . The difference between the two years is .)
- 3 (Incorrect. You may have found the difference for each month and added all these numbers, treating July as if it had an increase. You need to subtract that amount. Another way is to find the sum of the heights of the 2009 bars and subtract this from the sum of the heights of the 2010 bars.)
- 0.5 (Incorrect. It is possible that you found the difference between the amounts of rain for the month of June only.)
- 10.5 (Incorrect. This is the total rainfall for the summer of 2010, not the difference between the two years. Find the sum of the heights of the 2009 bars and subtract this from the sum of the heights of the 2010 bars.)
A: 2

Q: A dean polled the sophomore class about their intended majors, then created this graph based on the data.

The number of students who chose ''Other'' is the same as the number who chose which other major(s)?
- Social Sciences and Math/Computer Science (CS) combined (Incorrect. These combined sections are close to, but smaller than, the ''Other'' section in size. So there are fewer students who chose these majors than chose ''Other.'')
- Math/Computer Science (CS) and Foreign Languages combined (Correct. The ''Other'' section is about one-fourth of the graph. The Math/Computer Science and Foreign Languages sections combined are also about one-fourth of the graph. So, combined, these two majors represent about the same number of students as are represented by the ''Other'' section.)
- Foreign languages, Math/Computer Science (CS), and Social Sciences combined (Incorrect. These combined sections are greater than one-fourth of the circle, so there are more students planning to major in these subjects than in ''Other.'')
- Sciences (Incorrect. The Science section is larger than the ''Other'' section, so the number of students is not equal to the number of students in the ''Other'' section.)
A: Math/Computer Science (CS) and Foreign Languages combined

Q: The following line graph shows the grocery bill of the Turner family for the past five weeks.

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

I  The Turner family spent at least $100 each week.

II  The Turner family's grocery bill was usually less than $200 each week.

III  The Turner family's grocery bill steadily increased over the five weeks.
- I 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 amount of the grocery bill, as shown on the vertical axis.)
- I and II (Correct. The points on the graph are all at heights above 100, so the Turner family always spent more than $100. Week 4 was the only time when the Turners spent $200; all other points are lower, so the family usually spent less than $200. Their bill went down and up over the five weeks so it did not steadily increase. Therefore, I and II are the true statements.)
- 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 amount of the grocery bill, as shown on the vertical axis.)
- II only (Incorrect. Although statement II is true, it is not the only true statement. Check the other two statements. Remember that the height of each point shows the amount of the grocery bill, as shown on the vertical axis.)
A: I and II

Q: The stem and leaf plot shows the number of minutes Cal talked on his phone each day for the past 14 days.

Which data set is represented by this plot?
- 0, 5, 11, 15, 26, 45, 46, 52, 60, 71, 84, 87 (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 6 occurs three times for the stem 4. This means that the number 46 occurs three times in the original collection of numbers.)
- 0, 5, 11, 15, 26, 45, 46, 46, 46, 52, 60, 71, 84, 87 (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 0 and 0 to make 0; the largest combines 8 and 7 to make 87.)
- 0, 6, 11, 17, 25, 48, 50, 51, 54, 62, 64, 64, 64, 78 (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, 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 0 and 0 to make 0; the largest combines 8 and 7 to make 87.)
- 0, 0, 1, 1, 2, 4, 5, 5, 5, 6, 6, 6, 6, 7 (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 0 and 0 to make 0; the largest combines 8 and 7 to make 87.)
A: 0, 5, 11, 15, 26, 45, 46, 46, 46, 52, 60, 71, 84, 87

Q: Bernice received the following scores on five science tests: 96, 77, 82, 91, and 89. Which of the following statements is true?
- The median of the set of scores is 82. (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 mean of the set is greater 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 mean of the set is less than the median. (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: 77, 82, 89, 91, 96. The median is 89. The mean of the set is less than the median.)
- The mode of the set of scores is 96. (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.)
A: The mean of the set is less than the median.

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

20, 15, 50, 85, 75, 60
- The range is 85 and the midrange is 55. (Incorrect. You may have thought that the range is 85 because 85 is the greatest value, but you must subtract the least value from the greatest value. The number 55 is the median of this collection, not the midrange. To find the midrange, you must add the least and greatest values and then divide by 2.)
- The range is 70 and the midrange is 50. (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 is 70 and the midrange is 50.)
- The range is 70 and the midrange is 35. (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. (Incorrect. You used the first and last numbers as they were listed (20 and 60) to determine the range and midrange, instead of using the least and greatest values.)
A: The range is 70 and the midrange is 50.

Q: Which of the following statements about the box-and-whisker plot below is not true?
- Both 72 and 99 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 72 and 99. Therefore, these are the least and greatest values of the set. So 72 and 99 are in the set. This statement is true.)
- The midrange of the data set shown is 85.5. (Incorrect. The box-and-whisker plot shows the greatest value of the data set to be 99 and the least value to be 72. Add these values together and divide by 2 to find the midrange: . This statement is true.)
- There are fewer data points in the lower two quartiles than in the upper 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.)
- The median of the data set shown is 81. (Incorrect. The line that divides the box of the box-and-whisker plot is located above 81 on the number line. This represents the median of the data set. This statement is true.)
A: There are fewer data points in the lower two quartiles than in the upper two quartiles.

Q: Violet takes a survey of the ages of people in the food court at the mall at 1 p.m. and at 6 p.m. on a Friday.

Violet wants to find the best time to try to sell vacation plans in a kiosk near the food court. Which statement best describes when Violet should try to sell these vacation plans, and why?
- At 1 p.m., because the median age at that time is 41, while the median age of the people at 6 p.m. is 18 (Correct. The data set for 1 p.m. has 35 numbers, and the number in the middle is 41, making this the median age. Because the data set for 6 p.m. has 35 numbers, and the number in the middle is 18, this is the median age for that time. So it is more likely that older customers, who will be more likely to consider buying a vacation plan, will be at the mall at 1 p.m., which makes it a better time for Violet to sell her plans.)
- At 6 p.m., because the average age of someone in the food court at that time is about 25 (Incorrect. You correctly found the mean age of the data set for the 6 p.m time in the food court. However, the mean age of the data set for the 1 p.m. time is about 39, so there will probably be more people in the food court at that time who might buy vacation plans. 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 25, for example, without anyone actually being around the age of 25.)
- At 1 p.m., because there are more people who have a job in the food court at this time (Incorrect. Violet's data does not indicate who has a job, so she should not schedule her selling time on this basis.)
- At 6 p.m., because the range of ages for this data set is less than the range of ages for the 1 p.m. data set (Incorrect. It is true that the range of ages for the data set for 6 p.m. is less than the range of ages for the data set for 1 p.m. But this information does not indicate how young or old the people are, or if they might be likely to buy a vacation plan.)
A: At 1 p.m., because the median age at that time is 41, while the median age of the people at 6 p.m. is 18

Q: A pet store owner surveys his customers about the number of pets they own. The results are below:

One pet: 25 respondents

Two pets: 43 respondents

Three pets: 19 respondents

Four or more pets: 13 respondents

The owner wants to create a graph to highlight the percentage of owners who have two pets. Which graph is the best choice for the owner to use to represent the data?
- histogram (Incorrect. A histogram is best used for something like the results of a test for an entire class (that is, when you are given a large collection of numbers that can be grouped into intervals, and you want to see how the numbers are spread out). It cannot be used to compare data in categories.)
- circle graph (Correct. The owner wants to compare the percentages of people giving the different responses. A circle graph is best for comparing when you have several categories and want to show parts to the whole, or percentages.)
- box-and-whisker plot (Incorrect. A box-and-whisker plot is best used to show the median of a large set of data, as well as the spread of the data. It divides the data into four equal-sized groups. It cannot be used to compare data that is given in groups of different sizes.)
- line graph (Incorrect. A line graph is best used to show continuous data or some type of change over time. The input and output in a line graph would both be numbers. In this problem, the input is a category and the output is a number.)
A: circle graph

Q: The graphs below were created by an advertising agency for the computer store TechPlus to show its average price on laptops and desktops compared to another computer store's prices.

Which of the following statements best explains how the advertising agency misrepresented the data?
- The graphs do not include tablet computers, so there is not enough information to compare their prices. (Incorrect. It is true that the graphs do not show the prices of tablet computers. It is possible that this distorts the picture (for example, if the price of tablets at TechPlus is much higher than at CompStar), but there is another way in which the comparison was definitely and largely misrepresented.)
- The graph for CompStar makes its prices appear much higher, but its prices are only a little higher. (Incorrect. It is true that the graph for CompStar makes its computer prices appear much higher than TechPlus's, but the prices are actually lower than TechPlus's.)
- The graphs were created with different colors. (Incorrect. Although the colors of the bars in the graphs are different, this is not relevant to the data being presented.)
- The graphs use different scales, making it appear that the prices at TechPlus are much lower than CompStar. (Correct. The graph for TechPlus does not begin at 0, while the graph for CompStar begins at 0. The cost of the computers is actually higher at TechPlus. When two graphs are comparing two data sets, the scales need to be consistent.)
A: The graphs use different scales, making it appear that the prices at TechPlus are much lower than CompStar.

Q: A spinner is divided into four 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 the same as the probability that it will point to blue. (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 yellow is less than the probability of the arrow pointing to blue, because the yellow section is smaller.)
- The probability that the arrow will point to red is (Incorrect. You may have thought that the probability would be because there are four sections. This would be the case if the sections were equal in size, but they are not. The probability of pointing to red is more than because red takes up more than of the circle.)
- The probability that the arrow will point to green is less than (Correct. There are four colors on the spinner, and the green section is the smallest, so it takes up less than of the circle. You would expect the arrow to point to green less than of the time.)
- The probability that the arrow will point to blue is 1. (Incorrect. You may have chosen this answer because the blue section of the spinner is the biggest. However, though the arrow is more likely to point to blue than to any other color, this outcome is still not certain, so the probability is less than 1.)
A: The probability that the arrow will point to green is less than

Q: For her softball uniform, Meredith has a green, white, or striped jersey. She also has white, green, or striped shorts. If Meredith chooses a jersey and shorts randomly, what is the probability that she will go to softball practice in a striped jersey and green shorts?
- 1 (Incorrect. You may have chosen the size of the event space instead of the probability of the event. Write out a list of every combination of jersey and shorts and count the number of possibilities to find the size of the sample space.)
A: (a choice with no text)
If wrong: Incorrect. You may have thought that because there are three jerseys and three pairs of shorts, the size of the sample space would be 6, but it is not. Write out a list of every combination of jersey and shorts and count the number of possibilities to find the size of the sample space.
If wrong: Incorrect. You may have thought that because the probability of choosing a striped jersey by itself is and the probability of choosing a pair of green shorts by itself is , you should add these numbers together. Instead, write out a list of every combination of jersey and shorts and count the number of possibilities to find the size of the sample space.
If right: Correct. The sample space is every color combination of jersey and shorts: (green, green) (green, white) (green, striped) (white, green) (white, white) (white, striped) (striped, green) (striped, white) (striped, striped) So the total number of possible outcomes is 9. There is one outcome in the event: (striped, green). So is the probability of the event.

Q: Hal and Renee play the following game: A bag has 11 tiles in it, each with a letter from the word probability on it. Hal and Renee take turns drawing a tile, recording the letter, and placing the tile back in the bag. Hal earns a point if he draws a vowel. Renee earns a point if she draws a consonant. They decide that the letter y can be a vowel or a consonant. Which statement best explains whether or not the game is fair?
- The game is fair because both Hal and Renee will get a point if the letter y is drawn. (Incorrect. It is true that Hal and Renee decided that y is a consonant and a vowel, so each player can get a point for drawing it. However, this answer does not take into account all possibilities. First you need to write out the event spaces: the vowels for Hal and the consonants for Renee. Count the letter y as an outcome in each event space. Then find the probabilities.)
- The game is fair because Hal and Renee have the same probability of drawing a winning letter. (Incorrect. You may have thought that these events have the same probability because they have similar descriptions. First you need to write out the event spaces: the vowels for Hal and the consonants for Renee. Count the letter y as an outcome in each event space. Then find the probabilities.)
- The game is not fair because the probability of Hal drawing a winning letter is greater than the probability of Renee drawing a winning letter. (Incorrect. You may have mistakenly compared fractions or simply gotten the incorrect probabilities. First you need to write out the event spaces: the vowels for Hal and the consonants for Renee. Count the letter y as an outcome in each event space. Then find the probabilities.)
- The game is not fair because the probability of Hal drawing a winning letter is less than the probability of Renee drawing a winning letter. (Correct. The size of the sample space is 11, because there are 11 possible tiles to choose from. List the event space for Hal winning a point: {o, a, i, i, y} List the event space for Renee winning a point: {p, r, b, b, l, t, y} The probability is of Hal drawing a winning tile. The probability of Renee drawing a winning tile is , which is greater.)
A: The game is not fair because the probability of Hal drawing a winning letter is less than the probability of Renee drawing a winning letter.