This is a long review. Attempt each style of question, but if you know how to do the question, move on to more challenging ones. DO NOT GO THROUGH THIS REVIEW QUESTION BY QUESTION! 1. Joel researched the average daily temperature in his town. Average Daily Temperature in Lloydminster, SK Month Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec. average daily temperature ( C) 10.0 17.5 5.0 3.7 10.7 14.3 20.1 14.0 9.8 4.8 5.8 14.8 Determine the mean and range of the data. 2. Environment Canada compiled data on the number of lightning strikes per square kilometre in Saskatchewan and Manitoba towns from 1999 to 2008. 2.03 1.31 0.25 1.03 1.20 0.17 0.99 1.01 0.24 0.94 0.92 0.09 0.86 0.71 0.05 0.81 0.63 0.01 0.80 0.58 0.00 0.72 0.49 0.52 0.43 0.46 0.40 If the interval width is 0.25 and starts at 0.00, how many intervals are there? 3. An apple orchard has 32 trees with these heights, given in inches. 116 90 91 99 114 110 124 102 82 89 104 102 95 105 118 118 110 97 92 93 91 116 101 101 116 86 101 83 117 93 132 104 If the interval width is 5 and starts at 80, how many intervals are there? Math 20-2 Statistics Review Page 1
4. Environment Canada compiled data on the number of lightning strikes per square kilometre in Saskatchewan and Manitoba towns from 1999 to 2008. 2.03 1.31 0.25 1.03 1.20 0.17 0.99 1.01 0.24 0.94 0.92 0.09 0.86 0.71 0.05 0.81 0.63 0.01 0.80 0.58 0.00 0.72 0.49 0.52 0.43 0.46 0.40 Complete the frequency table. Lightning Strikes (per square kilometre) 0.00 0.49 0.50 0.99 1.00 1.49 1.50 1.99 2.00 2.49 Frequency 5. Environment Canada compiled data on the number of lightning strikes per square kilometre in Ontario towns from 1999 to 2008. 3.60 2.11 0.96 0.65 3.47 2.04 0.90 0.65 2.53 1.90 0.85 0.65 2.38 1.90 0.72 0.63 2.25 1.33 0.70 0.38 2.25 1.13 0.66 0.19 Complete the frequency table. Lightning Strikes (per square kilometre) 0.00 0.99 1.00 1.99 2.00 2.99 3.00 3.99 Frequency Math 20-2 Statistics Review Page 2
6. Environment Canada recorded the amount of rain (in millimetres) in Lloydminster, SK for two months. 3.8 19.4 46.0 0.6 3.2 3.2 1.3 2.6 4.2 1.0 2.2 7.8 1.6 0.4 0.2 5.2 If the interval width is 10 and starts at 0, what is the last interval? 7. A company measured the lifespan of a random sample of 40 batteries in their MP3 players. Times are in hours. 7.8 11.0 10.5 8.8 9.1 9.4 11.2 9.4 8.6 9.0 9.3 8.5 7.9 9.1 7.1 9.3 9.4 9.7 10.6 8.5 9.2 8.2 7.4 8.8 8.6 8.0 8.0 11.1 9.2 11.4 8.2 9.6 8.5 10.5 10.7 9.5 11.4 8.2 9.7 8.5 Suppose you wanted fewer than 10 intervals. What interval width would give a good representation of how the data is distributed? 8. A company measured the lifespan of a random sample of 40 batteries in their MP3 players. Times are in hours. 7.8 11.0 10.5 8.8 9.0 9.4 10.2 9.4 8.6 9.0 9.3 8.5 7.9 9.1 7.9 9.3 7.4 9.7 10.6 8.5 9.2 13.2 7.4 8.8 7.6 8.0 8.0 11.1 9.2 11.4 8.2 9.6 8.5 10.5 10.7 9.5 10.4 8.2 9.7 8.5 Complete the frequency table. Battery Lifespan (h) 7.0 7.9 8.0 8.9 9.0 9.9 10.0 10.9 11.0 11.9 12.0 12.9 13.0 13.9 Frequency Math 20-2 Statistics Review Page 3
9. At the end of a bowling tournament, three friends analyzed their scores. Lucia s mean bowling score is 144 with a standard deviation of 12. Zheng s mean bowling score is 88 with a standard deviation of 6. Kevin s mean bowling score is 108 with a standard deviation of 5. Who is the more consistent bowler? 10. Four groups of students recorded their pulse rates after a 2 km run. Group 1 126 168 158 192 146 166 104 164 116 138 172 136 152 128 Group 2 158 132 156 160 108 150 178 136 172 140 126 154 130 160 Group 3 136 174 156 176 150 166 142 156 130 182 180 166 148 172 Group 4 144 150 142 152 174 176 118 152 178 164 128 158 158 166 Determine the standard deviation of Group 1, to one decimal place. 11. Four groups of students recorded their pulse rates after a 2 km run. Group 1 126 168 158 192 146 166 104 164 116 138 172 136 152 128 Group 2 158 132 156 160 108 150 178 136 172 140 126 154 130 160 Group 3 136 174 156 176 150 166 142 156 130 182 180 166 148 172 Group 4 144 150 142 152 174 176 118 152 178 164 128 158 158 166 Determine the standard deviation of Group 2, to one decimal place. 12. Four groups of students recorded their pulse rates after a 2 km run. Group 1 126 168 158 192 146 166 104 164 116 138 172 136 152 128 Group 2 158 132 156 160 108 150 178 136 172 140 126 154 130 160 Group 3 136 174 156 176 150 166 142 156 130 182 180 166 148 172 Group 4 144 150 142 152 174 176 118 152 178 164 128 158 158 166 Determine the standard deviation of Group 3, to one decimal place. Math 20-2 Statistics Review Page 4
13. An apple orchard has 32 trees with these heights, given in inches. 116 90 91 99 114 110 124 102 82 89 104 102 95 105 118 118 110 97 92 93 91 116 101 101 116 86 101 83 117 93 132 104 Determine the standard deviation, to one decimal place. 14. Shaydan and Milena are laying interlocking bricks. Their supervisor records how many bricks they lay each hour. Hour 1 2 3 4 5 6 Shaydan 186 164 166 172 182 175 Milena 166 174 159 172 165 176 Which worker is more consistent? 15. The ages of members in a hiking club are normally distributed, with a mean of 32 and a standard deviation of 6 years. What percent of the members are between 26 and 32? 16. The ages of members in a hiking club are normally distributed, with a mean of 32 and a standard deviation of 6 years. What percent of the members are younger than 20? 17. A teacher is analyzing the class results for a computer science test. The marks are normally distributed with a mean (µ) of 79.5 and a standard deviation (σ) of 3.5. Determine Daryl s mark if he scored µ + σ Math 20-2 Statistics Review Page 5
18. A teacher is analyzing the class results for a computer science test. The marks are normally distributed with a mean (µ) of 77.4 and a standard deviation (σ) of 4.2. Determine Sina s mark if she scored µ + 2.5 σ. 19. A teacher is analyzing the class results for a computer science test. The marks are normally distributed with a mean (µ) of 79.5 and a standard deviation (σ) of 3.5. Sketch the normal curve for the test. 20. Is the data in this set normally distributed? Explain. Interval 10 19 20 29 30 39 40 49 50 59 60 69 Frequency 1 8 11 13 9 3 21. Is the data in this set normally distributed? Explain. Interval 1 5 6 10 11 15 16 20 21 25 26 30 Frequency 2 9 22 35 15 6 22. Determine the z-score for the given value. x μ µ = 9.3, σ = 0.4, x = 8.8 z = σ Math 20-2 Statistics Review Page 6
23. Determine the z-score for the given value. µ = 52.9, σ = 1.7, x = 58.2 24. Determine the percent of data to the left of the z-score: a. z = 1.05 b. z = 0.71 25. Determine the percent of data to the right of the z-score: z = 0.68. 26. Determine the percent of data between the following z-scores: a. z = 0.68 and z = 1.74 b. z = 0.34 and z = 1.70. 27. Yumi always waits until her gas tank is nearly empty before refuelling. She keeps track of the distance she drives on each tank of gas. The distance varies depending on the weather and the amount she drives on the highway. The distance has a mean of 520 km and a standard deviation of 14 km. a) What percent of the time does she drive between 534 km and 562 km on a tank of gas? b) Between what two symmetric values will she drive 95% of the time? Math 20-2 Statistics Review Page 7
28. Jackson raises Siberian husky sled dogs at his kennel. He knows, from the data he has collected over the years, which the masses of adult male dogs are normally distributed, with a mean of 23.6 kg and a standard deviation of 1.8 kg. Jackson has 48 puppies this year. How many of them could he expect to have a mass greater than 20 kg when they grow up? 29. A hardware manufacturer produces bolts that have an average length of 1.22 in., with a standard deviation of 0.02 in. To be sold, all bolts must have a length between 1.20 in. and 1.25 in. What percent, to the nearest whole number, of the total production can be sold? Math 20-2 Statistics Review Page 8