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MDM 4U: Chapter 3 Review Question 1: Match up the Distributions with the correct Classifications: (there may be more than one classification that applies to each distribution) a) Bimodal i) iv) ii) v) iii) vi) b) U-shaped c) Uniform d) Mound-shaped e) Right-Skewed f) Left-Skewed g) Symmetrical Question 1 Answer: i) (c) (g) ii) (a) (b) (g) iii) (f) iv) (a) (b) (g) v) (d) (g) vi) (e) Question 2: What is wrong with the following histograms? What would make them better? a) b) Question 2 Answer: In (a) there are too many intervals as there are frequencies of 0. It looks too much like a bar graph. In (b) there are too few intervals. There should be at least 5 intervals Question 3: Are the following statements true or false? a) The median is not useful if the data contains outliers. b) The mode is the most frequent value or interval c) The mean can be represented by : 𝑥̅ or by 𝜇 d) The median is useful if the distribution is skewed. e) The mean is not affected by outliers. f) The mode is the only appropriate measure of central tendency for qualitative data. g) The median is the midpoint that divides the data into sets that are not equal. h) The mean, median, and mode are all types of central tendency i) To find the median the data points must be in order from lowest to highest or highest to lowest. j) There is always a mode in every set of data. Question 3 Answer: a) FALSE b) TRUE c) TRUE d) TRUE g) FALSE i) TRUE j) FALSE h) TRUE e) FALSE f) TRUE Question 4: Calculate the range, quartiles, interquartile range, and the standard deviation of the following data sets. a) 1 3 3 5 6 6 7 7 7 8 b) 10 __ 16 20 __ 50 60 __ 70 90 c) 1 __ __ __ 7 8 9 11 12 __ __ __ 16 18 25 29 31 __ __ 3 4 __ __ __ 6 6 6 6 6 6 6 7 8 10 __ __ 18 24 28 16 d) 0 6 9 Road Block: Relay Each person from the group must complete one of the letters. Each team member must complete their letter on their own. No one in the group is allowed to speak as each group members works. The group member who calculates the values for (a) must check their solution. Once they have received the okay, that their solutions are correct, then they will receive the values that are missing from the next part of the question (aka the values missing for (b)). And so on. Question 4 Answer: a) Range = 8 Q1 = 3 Q2 = 6 Q3 = 7 IQR = 4 s.d. = 2.42 or 2.3 Q3 = 68 IQR = 52 s.d. = 28.4 or 26.9 Q3 = 16 IQR = 9 s.d. = 8.4 or 8.14 Q3 = 9 IQR = 4 s.d. = 6.7 or 6.5 MISSING NUMBERS for (b) : 14, 30, 68 b) Range = 80 Q1 = 16 Q2 = 40 MISSING NUMBERS: 5, 5, 5, 15, 15, 15, c) Range = 30 Q1 = 7 Q2 = 13.5 MISSING NUMBERS: 2, 2, 5, 5, 5, 12, 12 d) Range = 28 Q1 = 5 Q2 = 6 Question 5: If the mass of 35 dogs in your neighbourhood were normally distributed, with a mean of 11.2 kg and a standard deviation of 2.8, how many dogs would you expect to have a mass: a) Between 8.4 kg and 14 kg? b) Between 5.6 kg and 16.8 kg? c) Between 2.8 kg and 19.6 kg? d) 11.2 kg or less? Question 5 Answer: a) 1 s.d. away from the mean 68% 0.68(35) = 23.8 = 24 dogs b) 2 s.d. away from the mean 95% 0.95(35) = 33.25 = 33 dogs c) 3 s.d. way from the mean 99.7 % 0.997(35) = 34.895 = 35 dogs d) Since 11.2 is the mean then 50% 0.5(35) = 17.5 = 18 dogs Question 6: Flooring materials being produced at a lumber mill follow a normal distribution of X~N(7.9mm, 0.4mm2 ). a) What range do about 68% of the flooring materials fall within? b) If you wanted 95% of the material to fall within the range of 7.7 mm and 8.15 mm, what mean and standard deviation would be required. Question 6 Answers: a) 86% is 1 s.d. away from the mean 7.9 + 0.4 = 8.3; 7.9 – 0.4 = 7.5 Therefore the range is 7.5 <= x <= 8.3 b) 95% is 2 s.d. away from the mean 7.7 <=x <= 8.15 7.7 + 8.15 / 2 = 15.85/2 = 7.925 7.925-7.7 = 0.225 8.15 – 7.925 = 0.225 Therefore the mean would need to be 7.925 and the standard deviation would be 0.225 Question 7: For the distribution X~N(14, 42) determine the number of standard deviations each piece of data lies above or below the mean. a) X = 11 b) X = 21.5 c) 14.25 b) 1.875 s.d. above the mean c) 0.0625 s.d. above the mean Question 7 Answers: a) 0.75 s.d. below the mean Question 8: Perch in a lake have a mean length of 20 cm and a standard deviation of 5 cm. Find the percent of the population that is less than or equal to the following lengths. a) 22 cm b) 16 cm c) 28 cm d) 4 cm b) 21.19% c) 94.52% d) 0% Question 8 Answers: a) 65.54%