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Maths Quest Maths B Year 11 for Queensland Chapter 10 Summary statistics WorkSHEET 10.1 WorkSHEET 10.1 Summary statistics 1 These data give the amount of weekly pocket money given to a student for 8 weeks: Name: ___________________________ 2 Find the mean of the pocket money. (b) Find the median of the pocket money. (c) Find the mode of the pocket money. This frequency table shows the sick days taken by the workers in a factory in a month. Mean = (b) $5.00, $5.20, $5.80, $5.90, $6.40, $6.50, $6.80, $6.80 $5.90 $6.40 Median = 2 = $6.15 (c) Mode = $6.80 (a) (b) (c) Find the mean number of sick days per worker. Find the median number of sick days per worker. Find the mode for the number of sick days. 4 5 Number of sick Frequency days (x) (f) 0 8 1 6 2 4 3 2 4 4 5 3 6 3 Totals 30 Number of sick Frequency days (f) 0 8 1 6 2 4 3 2 4 4 5 3 6 3 (a) Sum of 8 weeks' pocket money 8 $48.40 = 8 = $6.05 (a) $5.80, $6.40, $5.00, $6.50, $6.80, $5.90, $6.80, $5.20. (a) 1 fx 0 6 8 6 16 15 18 69 69 30 = 2.3 sick days per worker. Mean = (b) Median = 2 (c) Mode = 0 Maths Quest Maths B Year 11 for Queensland 3 This grouped frequency table shows the area of (a) farm lots in hectares. Area (ha) 30405060708090- (a) (b) (c) (d) 4 Chapter 10 Summary statistics WorkSHEET 10.1 Frequency 3 2 8 6 3 1 2 Add the midpoint x, frequency times midpoint f x and cumulative frequency columns to the table. Write down the sum (c) of f and f x columns. (d) Find the mean area of the farm lot. Find the median area of the farm. Find the mode. Find the range of each of the following sets of data. (a) 2, 5, 4, 5, 7, 4, 3 (b) 103, 108, 111, 102, 111, 107, 110 (c) 2.5, 2.8, 3.4, 2.7, 2.6, 2.4, 2.9, 2.6, 2.5, 2.8 5 Frequency Area (ha) (f) 303 402 508 606 703 801 902 Totals 25 (b) 2 Midpoint (x) 35 45 55 65 75 85 95 fx 105 90 440 390 225 85 190 1525 Cumulative frequency 3 5 13 19 22 23 25 1525 25 = 61 ha Mean = Median group is 50–60 ha Modal group is 50–60 ha (a) Range = 7 – 2 =5 (b) Range = 111 – 102 =9 (c) Range = 3.4 – 2.4 =1 3 Maths Quest Maths B Year 11 for Queensland 5 Chapter 10 Summary statistics WorkSHEET 10.1 Use the frequency distribution tables below to find the range for each of the following sets of scores. (a) Score Frequency 89 12 90 25 91 36 92 34 93 11 94 9 95 4 3 2 (a) Range = 95 – 89 =6 (b) Range = 180 – 150 = 30 (b) Class 150 – 155 155 – 160 160 – 165 165 – 170 170 – 175 175 – 180 6 7 Frequency 12 25 38 47 39 20 The number of goals scored by a team is shown 4, 4, 5, 5, 7, 9, 12, 14, 16, 16 below: (a) Lower quartile = 5 5, 4, 4, 7, 5, 9, 12, 14, 16, 16. (b) Upper quartile = 14 (a) Find the lower quartile. (b) Find the upper quartile. (c) Find the interquartile range The stem-and-leaf plot below gives the exact masses of 24 packets of biscuits. Find the interquartile range of the data. Key: 248 | 4 = 284.4 g Stem | Leaf 248 | 4 7 8 249 | 2 3 6 6 250 | 0 0 1 1 6 9 9 251 | 1 5 5 5 6 7 252 | 1 5 8 253 | 0 (c) 3 Interquartile range = 14 5 =9 Lower quartile = 249.6 Upper quartile = 251.55 Interquartile range = 251.55 – 249.6 = 1.95 3 Maths Quest Maths B Year 11 for Queensland 8 Chapter 10 Summary statistics WorkSHEET 10.1 Use your calculator to find the standard deviation of the set of outcomes when a six-sided die is rolled as shown below. Standard deviation = 1.87 4 1 1, 2, 3, 4, 5, 6 State your answer correct to 2 decimal places. 9 A supermarket chain is analysing its sales over a week. The chain has 15 stores and the sales for each store for the past week were ( in $million): 1.5 2.1 1.4 1.6 10 2.4 2.0 1.8 1.1 0.7 1.2 0.8 1.7 0.9 1.3 3 1.1 (a) x = 1.44 (b) Population, as the sales from every store are considered. (a) Calculate the mean sales for the week. (b) Should the population or sample standard (c) deviation be used in this case? (c) What is the value of the appropriate standard deviation? = 0.48 The following frequency distribution gives the x = 1825 prices paid by a car wrecking yard for a sample s = 797.03 of 40 car wrecks. Price ($) 0 – 500 500 – 1000 1000 – 1500 1500 – 2000 2000 – 2500 2500 – 3000 3000 – 3500 Frequency 2 4 8 10 7 6 3 Find the mean and standard deviation of the price paid for these wrecks. 2