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3.2 – Measures of Central Tendency – Worksheet MDM4U Jensen 1) Use technology to calculate the mean, median, and mode for the following data sets. a) Marks on a set of tests {66, 65, 72, 78, 93, 70, 68, 64} b) Monthly rent ($) {625, 750, 800, 650, 725, 850, 625, 650, 625, 1250} c) Survey responses (1 = never, 2 = sometimes, 3 = often, 4 = always) d) Waiting time, in minutes, at a fast-­‐food restaurant {5, 5.5, 6.5, 7, 7.5, 7, 7, 5, 6.5, 5, 5, 8.5, 0.5, 4.5, 7} e) Points scored by a basketball player {12, 15, 8, 12, 15, 10, 3, 14, 15} f) Daily sales totals ($) {0, 0, 0, 17 000, 0, 0, 28 455, 0, 0, 41 590} 2) Use the relative location of the mean, median, and mode calculated in Question 1 to describe the sets as symmetric, skewed left, or skewed right. a) b) c) d) e) f) 3) Hakim’s Shoes reported the following sales results: 4 5 6 7 8 9 10 Size Frequency 5 11 15 18 a) Calculate the mean, median, and mode shoe size. b) Which measure of central tendency is most appropriate? Why? 4) Match each distribution with its mean, median, and mode. a) mean: 6.2 median: 6 mode: 3.8 b) mean: 6 median: 6 mode: 10, 2 c) mean: 6 median: 6 mode: 6 d) mean: 8.1 median: 8.5 mode: 10 i) ii) iii) 19 13 iv) 7 5) A pair of dice is rolled numerous times. The sum of the dice, as well as the frequency, is recorded. Calculate the mean, median, and mode for the results. 2 3 4 5 6 7 8 9 10 11 12 Sum 2 3 5 7 9 11 8 7 4 2 1 Frequency 6) Jasmine records the dates on 125 pennies. Find the mean and find the median modal interval of the pennies. 1990 -­‐ 1999 1980 -­‐1989 1970 -­‐ 1979 1960 -­‐ 1969 Date 56 42 21 6 Frequency 7) A student’s term mark is 75. The term mark counts for 70% of the final mark. What mark must the student achieve on the exam to earn a final mark of… a) at least 70? b) 75 c) 85 8) The chart to the right represents the distribution of salaries at a local company. a) Calculate the median and modal salary interval b) Calculate the weighted mean salary. Answers 1) a) mean = 72, median = 69, no mode b) mean = $755, median = $687.50, mode = $625 c) mean = 2.7, median = 3, mode = 3 d) mean = 5.8, median = 6.5, mode = 5, 7 e) mean = 11.6, median = 12, mode = 15 f) mean = 8704.5, median = 0, mode = 0 2) a) skewed right b) skewed right c) symmetric d) skewed left e) skewed left f) skewed right 3) a) mean = 7.2, median = 7, mode = 8 b) mode tells you the most popular size 4) a) ii b) iii c) I d) iv 5) mean = 6.78, median = 7, mode = 7 6) mean = 1986.84 or 1987, median = 1980-­‐1989, mode = 1990-­‐1999 7) a) at least 58.4 b) 75 c) 108.4 (therefore not possible) 8) a) median = 24000-­‐26999, mode = 21000-­‐23999 b) 26074.47