MDM4U Grade 12 Statistics of One Variable Test 5

Matching Match these terms with the descriptions below. a. cluster sample c. voluntary-response sample b. multi-stage sample d. convenience sample 1. An easily accessible sample is chosen. ______Answer: D 2. Two or more levels of random sampling are used. ______Answer: B 3. The population is invited to respond. ______Answer: C 4. Samples are randomly selected from representative groups. ______Answer: A

Match each statement below to one of the following measures of central tendency. a. mean b. median c. mode 5. It is the most familiar and most commonly used measure. ______Answer: A 6. It may not exist in some sets of data. ______Answer: C 7. It is the least commonly used measure. ______Answer: C 8. It is a computed measure whose value is affected by all of the values in a set of data. ______Answer: A 9. Its value can be greatly influenced by outliers. ______Answer: A 10. It divides a set of data into two groups with equal numbers of values. ______Answer: B Short Answer 11. What is wrong with the intervals in the following table?

Height (cm) Frequency 60–62 6 63–65 18 66–69 44 69–75 10

Answer: The last two intervals overlap. Also, the intervals have three different widths, so it is not possible to make direct comparisons of the frequencies.

12. Can a discrete variable have non-integer values? Support your answer with an example. Answer: Yes. Examples may vary. Half-sizes for shirts and shoes are two everyday examples.

13. A television reporter interviewed travelers stranded at an airport during a snowstorm about the efficiency of air travel in Canada. Name the sampling techniques used. Answer: Convenience sample

14. How could you use a graphing calculator to select a random sample? Answer: Answers may vary. One method is to assign numbers to the population and then use the randint (command to make random selections.

15. How could you use a spreadsheet to select a random sample? Answer: Answers may vary. One method is to assign numbers to the population and then use the RANDBETWEEN or RANDINT functions to make random selections.

16. Give an example of a survey with a) sampling bias b) non-response bias Answer: Answers will vary. Here are two simple examples: a) A survey conducted by e-mail will miss households that do not have computers. b) If a telephone survey is conducted only in English, people who do not speak it fluently might choose not to participate.

17. Identify the type of bias in these survey questions and reword them to remove the bias. a) Which is less damaging to the environment: hydro-electric power or nuclear power with its highly radioactive wastes? b) Do you really think fast food can be nutritious? Answer: loaded questions a) Which is less damaging to the environment: nuclear power or hydro- electric power? b) Can fast food be nutritious?

18. Identify the type of bias in these survey questions and reword them to remove the bias. a) Do you think that small, yappy dogs make good pets? b) Destruction of the rain forest in Brazil occurs at a rate of about 14 000 km2/year. Should logging be restricted in Canada? Answer: loaded questions a) Do small dogs make good pets? b) Should logging be restricted in Canada?

19. The numbers of service calls a heating company made during the first 11 days of October are listed below. Find the mean, median, and mode for this set of data: 6, 28, 28, 11, 30, 21, 17, 25, 28, 28, 20. Answer: mean 22, median 25, mode, 28 20. The numbers of houses a real-estate agency sold each month from January to October are listed below. Calculate the mean, median, and mode for these sales figures. 8, 3, 16, 6, 24, 13, 16, 16, 2, 16. Answer: mean 12, median 14.5, mode 16 21. The mean of the values 9, 11, 13, 21, 24, 18, and d is 17. Find d. Answer: 23 22. Each child in a study of infantile autism was given a behavioural test and graded on a scale from 0 (no symptoms) to 116 (maximum severity). The scores of the 21 children in the study were as follows: 27, 35, 65, 67, 47, 46, 63, 44, 34, 51, 17, 40, 41, 60, 24, 48, 29, 73, 60, 41, 47. Calculate the mean score, the standard deviation, and the variance. Answer: Since the study is trying to determine the characteristics of the population of all autistic children, use the formulas for calculating statistics for a sample. = 45.7, s = 15.1, s2 = 229

A consumer magazine evaluated 39 models of bathroom scales. The table below lists the prices for these models (rounded to the nearest dollar).

Scale Model Price ($) Scale Model Price ($) EconoHealth A10 50 Superskale 6400 65 EconoHealth A12 50 Superskale 7200 20 EconoHealth B10 50 Superskale 8000 14 EconoHealth E10 28 Superskale 8280 25 EconoHealth Digital-10 65 SvelteChek 12300 24 EconoHealth E-20 40 SvelteChek 12400D 48 EconoHealth E-30 50 SvelteChek 12509 15 HealthSkale 190 22 SvelteChek 12510 10 HealthSkale 210 32 SvelteChek Fashion 17 HealthSkale 211 30 SvelteChek Pro 50 HealthSkale 290 Deluxe 79 SvelteChek Xtra 25 HealthSkale 310 50 Weighbeter 550 22 HealthSkale 1000 23 Weighbeter 801D 60 HealthSkale 1002 20 Weighbeter 830 30 HydroXact 12573 35 Weighbeter 835 30 HydroXact 12756 24 Weighbeter 950 10 HydroXact 12856 25 Weighbeter 2000 12 Prowt P10A 120 Weighbeter 2100 20 Prowt Value 35 Weighbeter Basic 12 Prowt Value 2 35 23. What is the z-score for the price of a) the Weighbeter 801D scale? Answer: a) 1.13 b) the Weighbeter 830 scale? Answer: b) –0.24

24. What is the z-score for the price of a) the EconoHealth E10 scale? Answer: a) –0.33 b) the HydroXact 12573 scale? Answer: b) –0.0082 c) the Prowt P10A scale? Answer: c) 3.85

Problem 25. The table below shows the lengths of ski poles sold by a sporting goods store last December. Create a histogram and frequency polygon to display this information. Length (cm) Frequency 125–129 6 130–134 18 135–139 44 140–144 10 145–149 5 Answer: 26. For a science project, a student tested how long 16 samples of heavy- duty batteries would power a portable CD player. Here are the running times, in hours: 29, 26, 23, 22, 22, 17, 27, 25, 22, 22, 23, 22, 27, 23, 24, 26 a) Determine the range for these data. Answer: 12 b) Determine a reasonable interval size and the number of intervals. Answer: Answers may vary. Two of the better choices are five 3-h intervals or seven 2-h intervals. c) Produce a frequency table for these data. Answer: Answers may vary.

27. As of 2002, the top ten movies in terms of gross earnings were as follows (figures rounded to the nearest million dollars).

Rank Movie Gross ($000 000) 1 Titanic 1836 2 Harry Potter and the Sorcerer's 962 Stone 3 Star Wars: The Phantom Menace 924 4 Jurassic Park 921 5 The Lord of the Rings: The 836 Fellowship of the Ring 6 Independence Day 813 7 Star Wars 798 8 The Lion King 767 9 E.T. the Extra-Terrestrial 757 10 Forrest Gump 680 a) Find the median, first quartile, and third quartile for these gross earnings. Answer: b) Calculate the range and interquartile range. Answer: c) Calculate the mean, standard deviation, and variance. Answer: d) What is the z-score for the gross earnings of The Lion King? Answer: e) What is the z-score for the gross earnings of Titanic? Answer: a) The median has a value halfway between the fifth and sixth highest gross earnings. Thus, the median is million dollars. The first quartile is the median of the lower half of the data and the third quartile is the median of the upper half, so Q1 = 767 million dollars and Q3 = 924 million dollars. b) The range is 1836 – 680 = 1156 million dollars. The interquartile range is Q3 – Q1 = 924 – 767 = 157 million dollars c) The ten top-grossing films are a separate population of unusually successful movies rather than a representative sample of all movies. Therefore, use the population formulas to calculate the mean, standard deviation, and variance: and d) For The Lion King, e) For Titanic,