2, 3, 4, 4, 5, 5, 5, 6, 6, 7 There is an even number of items, so find the mean of the middle two numbers.

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1 Find the mean, median, and mode for each set of data. Round to the nearest tenth, if necessary. 1. number of students in each math class: 22, 23, 24, 22, 21 Mean: The mean is 22.4 students. Median: Order the numbers from least to greatest. 21, 22, 22, 23, 24 The median number of students in the math classes is 22. Mode: There are two classes with 22 students, so the mode is 22 students. 2. grams of fat per serving: 2, 7, 4, 5, 6, 4, 5, 6, 3, 5 Mean: The mean is 4.7 grams of fat. Median: Order the numbers from least to greatest. 2, 3, 4, 4, 5, 5, 5, 6, 6, 7 There is an even number of items, so find the mean of the middle two numbers. The median number of grams of fat per serving is 5. Mode: Since 5 appears three times, the mode is 5 grams of fat per serving. 3. inches of rain last week: 1.5, 2, 2.5, 2, 1.5, 2.5, 3 Mean: The mean is approximately 2.1 inches. Median: Order the numbers from least to greatest. 1.5, 1.5, 2, 2, 2.5, 2.5, 3 The median number of inches of rain is 2. Mode: Since 1.5, 2, and 2.5 appear twice, the modes are 1.5, 2, and 2.5 inches of rain. esolutions Manual - Powered by Cognero Page 1

2 4. At the movie theater, six movies are playing and their lengths are 138, 117, 158, 145, 135, and 120 minutes. Which measure of center best represents the data? Justify your selection and then find the measure of center. Because there are no extreme values or numbers that are identical, the mean would best represent the data. Mean: The mean is minutes. Find the measures of variability and any outliers for each set of data. 5. The number of minutes spent reading each night: 31, 33, 32, 34, 35, 33 Range: The greatest value is 35 and the least value is 31. So, the range is or 4 minutes. Median, First Quartile, and Third Quartile: List the data from least to greatest. 31, 32, 33, 33, 34, 35 There is an even number of items, so find the mean of the middle two numbers. The median number of minutes spent reading each night is 33. The first quartile, or median of the lower half, is 32. The third quartile, or median of the upper half, is 34. The interquartile range is or 2. Outliers: To determine if there are any outliers, multiply the interquartile range, 2, by = 3 Subtract 3 from the first quartile and add 3 to the third quartile = 29; = 37 There are no values less than 29 or greater than 37, so there are no outliers. esolutions Manual - Powered by Cognero Page 2

3 6. The number of fish in each fish tank: 6, 5, 7, 8, 5, 6, 7, 9, 8, 6 Range: The greatest value is 9 and the least value is 5. So, the range is 9 5 or 4 fish. Median, First Quartile, and Third Quartile: List the data from the least to greatest. 5, 5, 6, 6, 6, 7, 7, 8, 8, 9 There is an even number of items, so find the mean of the middle two numbers. The median number of fish is 6.5. The first quartile, or median of the lower half, is 6. The third quartile, or median of the upper half, is 8. The interquartile range is 8 6 or 2. Outliers: To determine if there are any outliers, multiply the interquartile range, 2, by = 3 Subtract 3 from the first quartile and add 3 to the third quartile. 6 3 = 3; = 11 There are no values less than 3 or greater than 11, so there are no outliers. 7. Claire earned $5, $7, $10, $6, and $8 doing errands for her neighbors. Find the measures of variability and any outliers for the set of data. Range: The greatest value is 10 and the least value is 5. So, the range is 10 5 or $5. Median, First Quartile, and Third Quartile: List the data from the least to greatest. 5, 6, 7, 8, 10 The median amount Claire spent is $7. The first quartile, or median of the lower half, is or 5.5. The third quartile, or median of the upper half, is or 9. The interquartile range is or 3.5. Outliers: To determine if there are any outliers, multiply the interquartile range, 3.5, by = 5.25 Subtract 5.25 from the first quartile and add 5.25 to the third quartile = 0.25; = There are no values less than 0.25 or greater than 14.25, so there are no outliers. esolutions Manual - Powered by Cognero Page 3

4 8. The scores Mr. Han s students earned on their last test are shown in the table. Use the measures of variability to describe the data in the table. The greatest value is 99 and the least value is 58. So, the spread of the data, or range, is 41 points. The data ordered from the least to greatest is 58, 73, 74, 74, 74, 76, 76, 77, 80, 81, 82, 82, 82, 83, 84, 85, 86, 87, 88, 89, 92, 92, 99, and 99. There is an even number of items, so find the mean of the middle two numbers. The median test score is 82 points. The lower quartile, or median of the lower half, is or 76. One fourth of the students earned 76 points or less. The upper quartile, or median of the upper half, is or One fourth of the students earned 87.5 points or more. The interquartile range is or One half of the students earned between 76 and 87.5 points. Find the mean absolute deviation of each data set , 70, 75, 100 Find the mean. Find the absolute differences between each data value and the mean. Find the average of these differences. The average distance between each data value and the mean is esolutions Manual - Powered by Cognero Page 4

5 10. 0, 20, 175, 190, 175 Find the mean. Find the absolute differences between each data value and the mean. Find the average of these differences. The average distance between each data value and the mean is , 50, 40, 55, 45 Find the mean. Find the absolute differences between each data value and the mean. Find the average of these differences. The average distance between each data value and the mean is 6. esolutions Manual - Powered by Cognero Page 5

6 , 240, 300, 295, 280 Find the mean. Find the absolute differences between each data value and the mean. Find the average of these differences. The average distance between each data value and the mean is , 137, 156, 149 Find the mean. Find the absolute differences between each data value and the mean. Find the average of these differences. The average distance between each data value and the mean is 6. esolutions Manual - Powered by Cognero Page 6

7 14. The table shows the numbers of two colors of candies in several bags. Which data set has a greater mean absolute deviation? Justify your answer. Find the mean of the brown candies. Find the absolute value of the differences between each data value and the mean. Find the average of these differences. The mean absolute deviation of the brown candies is Find the mean of the red candies. Find the absolute value of the differences between each data value and the mean. Find the average of these differences. The mean absolute deviation of the red candies is The set of brown candies has a greater mean absolute deviation. esolutions Manual - Powered by Cognero Page 7

8 15. The double box plot shows the numbers of floors for buildings on two streets. Compare the centers and variations. Write an inference you can draw about the two populations. The median number of floors on Main St. is 40 with an interquartile range of 10. The median number of floors on Grand Ave. is 18 with an interquartile range of 5. Main St. has more variability and centers around a higher number of floors than Grand Ave. 16. To determine the weekly top ten songs, the local radio station asks people to log onto their Web site and vote for their favorite song. Identify the sample as biased or unbiased and describe its type. Explain. The sample is biased because it is a voluntary response survey. Only those people who are interested in participating in the survey are part of the sample. 17. Forty-five out of 60 people at a steakhouse said their favorite meal was steak. Is this sampling representative of the entire town? If so, how many of the 13,000 residents would say steak was their favorite meal? This is a biased, convenience sample because only customers in one restaurant specializing in steak were surveyed. So, this sampling method is not representative of the entire town. Mike rolls a ten-sided solid whose identical faces are numbered with the first ten square numbers. Find each probability. Then describe the likelihood of the event as impossible, unlikely, equally likely, likely, or certain. 18. P(ones digit is 2) sample space: {1, 4, 9, 16, 25, 36, 49, 64, 81, 100} favorable outcomes: none The probability is 0 or 0%. Because the probability of the event is 0%, the event is impossible. esolutions Manual - Powered by Cognero Page 8

9 19. P(two-digit number) sample space: {1, 4, 9, 16, 25, 36, 49, 64, 81, 100} favorable outcomes: 16, 25, 36, 49, 64, and 81 The probability is or 60%. Because the probability of the event is greater than 50%, the event is likely to occur. 20. P(multiple of 8) sample space: {1, 4, 9, 16, 25, 36, 49, 64, 81, 100} favorable outcomes: 16 and 64 The probability is or 20%. Because the probability of the event is less than 50%, the event is unlikely to occur. 21. P(ones digit not 3) sample space: {1, 4, 9, 16, 25, 36, 49, 64, 81, 100} favorable outcomes: 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100 The probability is 1 or 100%. Because the probability of the event is 100%, the event is certain. esolutions Manual - Powered by Cognero Page 9

10 22. P(odd) sample space: {1, 4, 9, 16, 25, 36, 49, 64, 81, 100} favorable outcomes: 1, 9, 25, 49, and 81 The probability is or 50%. Because the probability of the event is 50%, the event is equally likely to occur. 23. P(one-digit number) sample space: {1, 4, 9, 16, 25, 36, 49, 64, 81, 100} favorable outcomes: 1, 4, and 9 The probability is or 30%. Because the probability of the event is less than 50%, the event is unlikely to occur. 24. P(multiple of 5) sample space: {1, 4, 9, 16, 25, 36, 49, 64, 81, 100} favorable outcomes: 25 and 100 The probability is or 20%. Because the probability of the event is less than 50%, the event is unlikely to occur. esolutions Manual - Powered by Cognero Page 10

11 In a survey of randomly selected students, students chose their preference from among three meal options for a school event. 25. What was the experimental probability that a student chose burgers? 26. What was the experimental probability that a student chose the vegetarian option? 27. What was the experimental probability that a student chose either pizza or burgers? esolutions Manual - Powered by Cognero Page 11

12 28. Out of a similar group of 450 students, predict how many would choose the vegetarian option. Use the percent proportion to find 22% of 450. Out of a similar group of 450 students, 99 would choose the vegetarian option. A box contains 8 red markers, 5 green markers, and 5 blue markers. Once a marker is pulled from the box, it is replaced, and then another marker is pulled. Find each probability. 29. P(red, then green) When drawing the first marker, there are or 18 markers, and 8 of them are red. The first marker is replaced. When drawing the second marker, there are 18 markers, and 5 of them are green. The probability of drawing a red marker then a green marker is. 30. P(red, then red) When drawing the first marker, there are or 18 markers, and 8 of them are red. The first marker is replaced. When drawing the second marker, there are 18 markers, and 8 of them are red. The probability of drawing a red marker then a red marker is. esolutions Manual - Powered by Cognero Page 12

13 31. P(blue, then red) When drawing the first marker, there are or 18 markers, and 5 of them are blue. The first marker is replaced. When drawing the second marker, there are 18 markers, and 8 of them are red. The probability of drawing a blue marker then a red marker is. 32. P(green, then green) When drawing the first marker, there are or 18 markers, and 5 of them are green. The first marker is replaced. When drawing the second marker, there are 18 markers, and 5 of them are green. The probability of drawing a green marker then a green marker is. esolutions Manual - Powered by Cognero Page 13

14 33. P(blue, then blue) When drawing the first marker, there are or 18 markers, and 5 of them are blue. The first marker is replaced. When drawing the second marker, there are 18 markers, and 5 of them are blue. The probability of drawing a blue marker then a blue marker is. esolutions Manual - Powered by Cognero Page 14