Student: Date: Instructor: TODD CONKLIN Course: 3rd hour Math Assignment: Samples and Populations Practice/ End of Year Review 1. You ask 8 classmates how many pencils they have in their bags. The mean is 8 pencils. Calculate the mean absolute deviation for the number of pencils. Bag Contents 4 5 6 7 8 9 10 11 12 13 Number of Pencils The mean absolute deviation for the number of pencils is. (Round to the nearest integer as needed.) 2. You ask 8 classmates how many pencils they have in their bags. The mean is 9 pencils. Calculate the mean absolute deviation for the number of pencils. Bag Contents 4 5 6 7 8 9 10 11 12 13 Number of Pencils The mean absolute deviation for the number of pencils is. (Round to the nearest integer as needed.) 3. You think a coin is not fair. You have 10 friends each toss the coin 4 times and tell you the number of heads. The mean number of heads is 2.8. Find the mean absolute deviation of the data. Use pencil and paper. Explain how you can use the data to show that the coin is either fair or not fair. Number of Heads in Four Tosses 0 1 2 3 4 Number of Heads The mean absolute deviation is. (Type an integer or a decimal.) 4. Challenge For 20 days you count the number of cars in the school parking lot at the end of the day. You find the mean number of cars is 9.5. Calculate the mean absolute deviation of the data. Use pencil and paper. Find the mean of the deviations without doing any calculations. Explain how this indicates why you should use the mean of the absolute deviations instead. Number of Cars in the Parking Lot 6 8 10 12 The mean absolute deviation is. (Type an integer or a decimal.)
5. Think About the Process The following dot plots show the ages of two groups of tourists. The mean age of Group 1 is 45.1 years. The mean age of Group 2 is 45.3 years. What is the first step to finding the mean absolute deviation (MAD) for each group? What is the MAD for each group? Make a comparative inference based on the MAD values. Group 1 Group 2 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 Age (Years) 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 Age (Years) What is the first step to finding the mean absolute deviation (MAD) for each group? A. Find the mean of the minimum and maximum values that have dots. B. Find the middle number of all the dots. C. Find the difference from the mean for each value. D. Count the ages that have dots and find the mean of those numbers. The MAD for Group 1 is The MAD for Group 2 is years. (Type an integer or a decimal.) years. (Type an integer or a decimal.) Which of the following is a correct inference from the MAD values? A. The spread of ages is less for Group 1 than the spread of ages for Group 2. B. The spread of ages is greater for Group 1 than the spread of ages for Group 2. C. The spreads of ages are the same for Group 1 and Group 2. 6. The dot plots show the heights of two different types of plants in a greenhouse. Each dot represents the height of an individual plant. The mean height of Type A is 8 inches. The mean height of Type B is 11 inches. What is the mean absolute deviation for each type of plant? What conclusions can you make about the average height of the two types of plants? Type A Height Type B Height 4 5 6 7 8 9 10 11 1213 14 15 Inches 4 5 6 7 8 9 10 11 1213 14 15 Inches The mean absolute deviation for Type A is. The mean absolute deviation for Type B is. (Type integers or decimals.) What conclusions can you make about the average height of the two types of plant? A. The MAD for Type A is less than the MAD for Type B. There is a greater range in height for Type B plants. B. The MAD for Type A is greater than the MAD for Type B. There is a greater range in height for Type A plants. C. Both types have the same MAD and the same D. Both types have the same MAD and mean so the plants are very similar in average almost the same mean so the plants are very height. similar in average height.
7. What is the interquartile range of this box plot? -5 0 5 10 15 20 The interquartile range is. 8. The data set below shows the admission price (in dollars) for one-day tickets to 10 theme parks in the United States. What is the interquartile range of the data values? 57 63 41 44 28 48 62 42 40 41 The interquartile range is. 9. Mental Math Find the interquartile range of the data set. 83.8 38.7 65.9 95.7 72.4 41.7 11.4 20.1 57.6 The interquartile range is. 10. Writing The following box plots show the rainfall amounts over the past month in two major cities. What is the interquartile range (IQR) of the amounts of rainfall for each city? Make a comparative inference about the cities based on the IQR. Use pencil and paper. Make another comparative inference about these populations. Explain. City 1 City 2 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Rainfall (cm) 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Rainfall (cm) The interquartile range of the rainfall amounts for City 1 is. The interquartile range of the rainfall amounts for City 2 is. Make a comparative inference about the cities based on the IQR. Choose the correct answer below. A. The rainfall amounts for City 2 are more consistent than those for City 1. B. The rainfall amounts for City 1 and City 2 are equally consistent. C. The rainfall amounts for City 1 are more consistent than those for City 2.
11. Reasoning The following box plots show the amount of time students in two classes spent doing homework over the past month. What might you conclude about the populations based on the interquartile range? Use pencil and paper. Does the IQR or the range give a more accurate description of the data? Explain. Class 1 Class 2 25 26 27 28 29 30 31 32 33 34 35 Hours 20 22 24 26 28 30 32 34 36 38 40 Hours What might you conclude about the populations based on the IQR? A. Most of the students in Class 1 spend a similar amount of time on their homework. B. Most of the students in Class 1 and in Class 2 spend a similar amount of time on their homework. C. Most of the students in Class 2 spend a similar amount of time on their homework. 12. You are giving this box filled with fruit snacks to your friend as a gift. Find the volume of the box to find the amount of fruit snacks you can fit inside. Find the surface area of the box to find how much decorative wrap you need. 7 in. 4 in. 3 in. (The figure is not to scale.) The volume is in. 3. The surface area is in. 2. 13. An oval track is made by enclosing semicircles on each end of a 58 m by 116 m rectangle. Find the area enclosed by the track. Use 3.14 for π. 58 m 116 m 2 The area enclosed by the track is m. (Round to the nearest hundredth as needed.) 14. The figure shows the outline of a new pier that is going to be built at the ocean. What is the area of the pier? Use 3.14 for π. Use pencil and paper. Draw another figure which has the same area as the given figure. 48 m 48 m 96 m 2 The area of the pier is m. (Round to the nearest hundredth as needed.)
15. Find the total surface area and volume of the solid object shown to the right. 8.08' 16.5' The total surface area is ft 2. (Round to three significant digits.) The volume is ft 3. (Round to three significant digits.) 16. Find the volume of the figure. Approximate π by 3.14. 3 The volume of the figure is in. (Round to the nearest hundredth as needed.) 7 in 3 in 17. Reasoning The table shows the letter grades in math class for a random sample of 300 sixth grade students. Find the relative frequency for each letter grade to complete the table. Use pencil and paper. What additional information does the relative frequency give that the frequency doesn't? Explain. Letter Grades Grade Frequency Relative Frequency A 24 B 51 C 138 D 48 F 39 Total 300 1.00 Complete the table. Letter Grades Grade Frequency Relative Frequency A 24 (Simplify your answer.) B 51 (Simplify your answer.) C 138 (Simplify your answer.) D 48 (Simplify your answer.) F 39 (Simplify your answer.) Total 300 1.00
18. A survey asked 125 people to choose a number from 1 to 5. The results are shown in the table. What is the relative frequency for each number? Use pencil and paper. Predict the relative frequency for each number if 250 people were surveyed. Experiment Table Number 1 2 3 4 5 Number of Trials Frequency 15 25 30 35 20 125 The relative frequency for 1 is. The relative frequency for 2 is. The relative frequency for 3 is. The relative frequency for 4 is. The relative frequency for 5 is. 19. A fair coin is tossed two times in succession. The sample space is shown, where H represents a head and T represents a tail. Find the probability of getting exactly one tail. The probability of getting exactly one tail is.
20. Draw a tree diagram for choosing a vowel (a, e, i, o, u) and then a number (1, 2, or 3). Use the diagram to find the probability of choosing i and 2. Choose the correct tree diagram below. A. B. C. D. The probability of choosing i and 2 is. 21. Challenge You use a garden hose to fill a circular wading pool that is 81.9 cm deep. You measure the depth of the water in the pool every 3 minutes. The table shows the data. What is the rate of change of the depth of the water? What does the rate of change mean in this situation? How many minutes after the last measurement in the table will the pool be full? Filling a Wading Pool Time (minutes) 0 3 6 9 12 15 Depth of Water (cm) 0 6.3 12.6 18.9 25.2 31.5 The rate of change is. What does this rate of change mean? A. This is the depth of water needed to fill the pool for each minute. B. This is the number of minutes until the pool is full for each centimeter of water added. C. This is the number of minutes needed to add each centimeter of water to the pool. D. This is the depth of water the garden hose adds to the pool each minute. The pool will be full minutes after the last measurement. 22. A delivery truck drove 36 miles per hour. It took 3 hours to travel between two towns. What is the distance between the two towns? Use the equation d = rt, where d is distance, r is rate, and t is time. The distance between the two towns is miles. 23. Buying Posters Ann uses the equation y = 7.25x to calculate the total cost y in dollars for x posters. How much would she spend on 4 posters? She would spend $ on 4 posters.
24. Amelia needs to buy some dog food. At the nearest store, 6 bags of dog food cost $ 25.50. How much would Amelia spend on 3 bags of dog food? Amelia would spend $ on 3 bags of dog food. 25. Jeremy, Jean, and Sam are trying to see who runs the fastest. Jeremy says he can run 10 miles every hour. The table to the right shows the relationship between total miles Jean ran and time. The following graph shows the relationship for Sam. Who runs the fastest? Who runs the fastest? Jean Hours 2 3 4 5 Distance (miles) 20 30 40 50 100 y Sam A. They all run at the same speed. B. Jean runs the fastest. C. Sam runs the fastest. D. Jeremy runs the fastest. Distance (miles) 80 60 40 20 x 0 0 2 4 6 8 10 Time (hours) 26. Challenge Yesterday, Erik ran 3 1 2 miles in hour. Emily ran 2 1 3 3 miles in hour. Anna ran 3 miles in 4 3 2 5 4 5 hour. What was the unit rate for miles per hour for each person? Who ran the fastest? Use pencil and paper. 6 Describe two ways you can find who ran the fastest. The unit rate for Erik was mile(s) per hour. (Simplify your answer. Type an integer, proper fraction, or mixed number.) The unit rate for Emily was mile(s) per hour. (Simplify your answer. Type an integer, proper fraction, or mixed number.) The unit rate for Anna was mile(s) per hour. (Simplify your answer. Type an integer, proper fraction, or mixed number.) (1) ran the fastest. (1) Erik Emily Anna
27. To make green paint, you use 5 drops of yellow paint for every 6 drops of blue paint. Complete the table to show ratios equivalent to 5 : 6. Complete the table. Paint Ratios Drops of yellow 5 10 15 20 Drops of blue 6 Paint Ratios Drops of yellow 5 10 15 20 Drops of blue 6 28. For a school project, your group contains 2 boys and 3 girls. Complete the table to show ratios equivalent to 2 : 3. Complete the table. Group Ratio Boys 2 Girls 3 6 9 12 Group Ratio Boys 2 Girls 3 6 9 12 29. 1 A recipe calls for cup of ingredient A for every 1 1 cups of ingredient B. You use 4 cups of ingredient A. How many 2 5 cups of ingredient B do you need? You need cups of ingredient B. (Simplify your answer. Type an integer, proper fraction, or mixed number.) 30. Writing Ian 's car can go 96 miles on 3 gallons of gas. During a drive last weekend, Ian used 8 gallons of gas. How far did he drive? Use pencil and paper. Explain how the problem changes if you were given the distance Ian drove last weekend instead of how much gas he used. He drove miles. 31. If 5 sweaters cost $ 71.40, how much would 8 sweaters cost? The cost for 8 sweaters is $. 32. Set up and solve a proportion for the following application problem. If 4 pounds of grass seed cover 387 square feet, how many pounds are needed for 4257 square feet? pounds. 33. Tom makes $ 270.00 in 6 days. How much does he make in 2 days? Tom makes $ in 2 days.
34. You want to buy some beans. An 8 -ounce package costs $ 2.96. A 15 -ounce package costs $ 5.70. A 26 -ounce package costs $ 10.14. Which package is the best buy? The (1) -ounce package of beans is the best buy. (1) 8 26 15 35. Fundraising The ski team needs new uniforms. The students plan to sell plush toy eagles (the school mascot) for $5 each. The students find three companies on-line that sell stuffed mascots. Company A sells 18 eagles for $ 50.58. Company B sells 12 eagles for $ 33.36. Company C charges $ 45.28 for 16 eagles. Which company has the best buy? Company (1) has the best buy. (1) C B A 36. A supermarket was surveyed to find prices charged in various sizes. Find the best buy (based on the price per unit) for the item. SALAD DRESSING Size Price 16 oz $2.27 32 oz $3.01 48 oz $4.94 The best buy is the (1) -ounce size. (1) 32 48 16 37. The scale drawing of the truck is 13 inches long. What is the actual length of the truck? 1 inch=1.8 feet The gridlines are spaced 1 inch apart. The actual length of the truck is feet.
38. Find the unknown side lengths in similar triangles PQR and ABC. 35 Q a 15 B 25 R b P A 20 C a = (Simplify your answers. Type an integer or a fraction.) b = (Simplify your answers. Type an integer or a fraction.) 39. On a map, 1 inch equals 5 miles. Two cities are 4 inches apart on the map. What is the actual distance between the cities? The actual distance between the cities is miles. 40. The scale drawing is of a backyard tennis court. The scale is 1 cm = 2 m. What is the actual area of the tennis court? width 5.5 cm length 12 cm 2 The actual area of the tennis court is m. 41. Flooring How many square feet of flooring is needed to cover the entire kitchen floor? In the kitchen, square feet of flooring is needed to cover the entire floor. 1 inch=6 feet The gridlines are spaced 1 inch apart.
42. The pair of figures to the right are similar. The area of one figure is given. Find the area of the other figure to the nearest whole number. Area of smaller parallelogram = 12 ft 2 3 ft 9 ft The area of the larger parallelogram is ft 2. (Round to the nearest whole number as needed.) 43. The figures shown are similar. Find the lengths of x, y, and z. x y The length of side x is. (Type an integer or a decimal.) z 15 The length of side y is. (Type an integer or a decimal.) 40 The length of side z is. (Type an integer or a decimal.) 29 20 29 44. Use similar triangles and a proportion to find the length of the lake shown here. (Hint: The side 90 m long in the smaller triangle corresponds to side of 90 m + 110 m = 200 m in the larger triangle.) 45 m 90 m 110 m 200 m n = m 45. A triangle is formed by the building's height and shadow. Another triangle is formed by the flagpole's height and shadow. Using the following diagram, find the height of the building. 25 ft 42 ft 2 ft The height of the building is feet.