WORKSHEET General 2 Mathematics Topic Areas: Data and Statistics DS2/3/4 – Single Data Sets, Summary Stats and Interpretation Stem & Leaf, Box & Whisker Teacher: PETER HARGRAVES Source: HSC exam questions Exam Equivalent Time: 45 minutes Worked Solutions: Included Note: Each question has designated marks. Use this information as both a guide to the question's difficulty and as a timing indicator, whereby each mark should equate to 1.5 minutes of working (examination) time. Questions 1. Data, 2UG 2012 HSC 1 MC A set of scores is displayed in a stemandleaf plot. What is the median of these scores? (A) (B) (C) (D)
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WORKSHEET General 2 Mathematicsjschsmaths.weebly.com/uploads/5/...stem_and_leaf_+... · The stemandleaf plot represents the daily sales of soft drink from a vending machine. If the
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WORKSHEET General 2 MathematicsTopic Areas:Data and Statistics
DS2/3/4 – Single Data Sets, Summary Stats and Interpretation Stem & Leaf, Box & Whisker
Teacher: PETER HARGRAVESSource: HSC exam questionsExam Equivalent Time: 45 minutesWorked Solutions: IncludedNote: Each question has designated marks. Use this information as both a guide to the question's difficultyand as a timing indicator, whereby each mark should equate to 1.5 minutes of working (examination) time.
Questions
1. Data, 2UG 2012 HSC 1 MC
A set of scores is displayed in a stemandleaf plot.
What percentage of girls usually spend or less hours on the internet over aweekend? (1 mark)Jenny said that the graph shows that the same number of boys as girls usuallyspend between and hours on the internet over a weekend.
Under what circumstances would this statement be true? (1 mark)
6. Data, 2UG 2009 HSC 26a
In a school, boys and girls were surveyed about the time they usually spend on the internetover a weekend. These results were displayed in boxandwhisker plots, as shown below.
What is the modal travel time when he uses roads without tolls? (1 mark)
What is the median travel time when he uses roads without tolls? (1 mark)
Describe how the two data sets differ in terms of the spread and skewness of theirdistributions. (2 marks)
8. Data, 2UG 2013 HSC 26f
Jason travels to work by car on all five days of his working week, leaving home at eachday. He compares his travel times using roads without tolls and roads with tolls over a periodof working weeks.
He records his travel times (in minutes) in a backtoback stemandleaf plot.
Draw a boxandwhisker plot to display Kim’s results below that of Terry’s results. (1 mark)
What percentage of Terry’s results were below ? (1 mark)
Terry claims that his results were better than Kim’s. Is he correct? Justify youranswer by referring to the summary statistics and the skewness of the distributions. (4 marks)
9. Data, 2UG 2014 HSC 29c
Terry and Kim each sat twenty class tests. Terry’s results on the tests are displayed in the boxandwhisker plot shown in part (i).
The number of children aged 12–18 years is the same in both 2000 and 2010.
How many children were aged 12–18 years in 2000? (1 mark)
How many children aged 0–18 years are there in 2010? (1 mark)
Identify TWO changes in the distribution of ages between 2000 and 2010. In youranswer, refer to measures of location or spread or the shape of the distributions. (2marks)
What would be ONE possible implication for government planning, as aconsequence of this change in the distribution of ages? (1 mark)
10. Data, 2UG 2010 HSC 27b
The graphs show the distribution of the ages of children in Numbertown in 2000 and 2010.
♦ Mean mark 36%MARKER'SCOMMENT: Finding amedian proved challenging formany students. Remember thatfor an even number of values,average the middle two asshown.
♦♦ Mean mark 29%COMMENT: Examiners lookfavourably on using language oflocation in answers, particularlythe areas they have specificallypointed students towards(skewness in this example).
♦ Mean mark 35%MARKER'SCOMMENT: Markers arelooking for students to use thecorrect language of location andspread such as mean, median,interquartile range, standarddeviation and skewness.