Review Notes QuestionsExamples For fun

Displaying and Comparing Two

Data Sets

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1. Which expression is equivalent to 12k3 ÷ 4k ?a) 3k2

b) 3k3

c) 8k2

d) 8k3

2) What is the value of x + 2y if x = 5.6 and y = 3.1, correct to 2 decimal places?

8ya) 0.69b) 2.62c) 2.83d) 4.77

3) What is 0.000 000 326 mm expressed in scientific notation?a) 0.326 x 10-6 mmb) 3.26 x 10-7 mmc) 0.326 x 106 mmd) 3.26 x 107 mm

4) Which expression is equivalent to 3x2(x + 8) + x2 ?a) 3x2 + x2 + 8b) 3x3 + 25x2

c) 4x3 + 32x2

d) 24x3 + x2

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Displaying and Comparing Two Data Sets

Double stem-and-leaf plotsBy representing two related data sets in a double (back-to-back) stem-and-leaf display, similarities and differences, such as clustering and averages (measures of location), can be easily seen.

Box plotsWhereas a stem-and-leaf plot gives good visual comparison of the location of scores in a data set, a box plot (or box-and-whisker plot) shows the spread of the data. Find a five number summary and draw each box plot on the same scale.

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Double stem-and-leaf example:This double stem-and-leaf plot shows the numbers of dollars spent by a group of students visiting the Easter show. a) How many students went to the show? b) Give two observations on the shape and features of the data. c) Calculate the mean and standard deviation (to the nearest 5 cents) of amounts spent by boys and by girls.d) Considering all the information you have, do you think that boys are the bigger spenders? Why?

Answersa) 39 students, consisting of 20 boys and 19 girls. b) The amounts spent by the girls show clustering at $20-$29, whereas the amounts spent by the boys are more evenly spread out. The data for the girls is positively skewed. c) Girls: Mean = $25.80 Standard deviation σn-1 = $8.00 Boys: Mean = $30.10 Standard deviation σn-1 = $12.40d) Yes. The average amount spent by a boy was $30.10. This was about $6 more than the average amount spent by a girl.

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Box plot exampleThe box plots below show the ranges of unleaded petrol prices in six cities in Australia. a) i) which city's petrol prices had the smallest range? ii) Which city's had the largest range?b) In which city was petrol generally cheapest? Give a possible reason for this.c) Canberra, Sydney and Melbourne had the same range of prices. i) Which of these three cities had the lowest median price? ii) In which of these cities would you be more likely to pay a higher price for petrol?d) Write down one observation about petrol prices in Canberra.

Answersa) i) Adelaide ii) Darwinb) Brisbane. The government tax on petrol is lower than in the other cities and so the price paid by the consumer is lower. c) i) Sydney ii) Melbourned) They were evenly spread across the city. The distribution of petrol prices is symmetrical.

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Complete 4-05 questions 1-8

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3+5=8