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Box-Plots and 5-Number Summary, SM-Bank 016

Ellyse recorded the number of wickets she took in the first seven games of the cricket season, which are as follows:

  1. Complete the 5-number summary table of Ellyse's results below.   (2 marks)

  1. Draw a box plot, using the number line below for reference, that displays Ellyse's results.   (2 marks)
     

  1. Describe the skew of Ellyse's results.   (1 mark)

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Box Plots and 5-Number Summary, SM-Bank 015

Eli sat 22 Maths quizzes throughout year 8 and her results were recorded in the 5-number summary below.

  1. Using the number line below as reference, draw a box plot that displays Eli's results.   (2 marks)
     

  1. Describe the skew of Eli's results.   (1 mark)

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Box Plots and 5-Number Summary, SM-Bank 014

The test results in English and Mathematics for a class were recorded and displayed in the box plots.
 

  1. What is the interquartile range for English?   (1 mark)

  2. Compare and contrast the two data sets by referring to the skewness of the distributions and the measures of their centres and spread.   (3 marks)

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♦ Mean mark (ii) 35%
COMMENT: The best answers use the correct language of location and spread such as mean, median, interquartile range, standard deviation and skewness.

ii. 

Box Plots and 5-Number Summary, SM-Bank 013

Terry and Kim each sat twenty class tests. Terry’s results on the tests are displayed in the box plot shown in part (i).

  1. Kim’s  5-number summary for the tests is  67,  69,  71,  73,  75.

     

    Draw a box plot to display Kim’s results below that of Terry’s results.   (1 mark)
     
       

  2. What percentage of Terry’s results were below 69?     (1 mark)

  3. Describe the skew of Kim's results.   (1 mark)

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Box Plots and 5-Number, SM-Bank 011

Using a 5-number summary of the data represented in this graph, or otherwise, determine

  1. the range   (1 mark)

  2. the interquartile range   (2 marks)

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Box Plots and 5-Number, SM-Bank 010

Using a 5-number summary of the data represented in this graph, or otherwise, determine

  1. the median   (1 mark)

  2. the interquartile range   (2 marks)

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Box Plots and 5-Number, SM-Bank 009

Yoyo was practicing his cello for an orchestra audition and the data set below records the number of hours he practiced each day over a 10-day period.

Using a 5-number summary of this dataset, or otherwise, determine

  1. the range   (1 mark)

  2. the interquartile range   (2 marks)

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Box Plots and 5-Number, SM-Bank 008

Matt records the number of times he takes his dog Max for a walk each month. The data set below records the months January to August.

Using a 5-number summary of this dataset, or otherwise, determine

  1. the median   (1 mark)

  2. the interquartile range   (2 marks)

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Box Plots and 5-Number, SM-Bank 005

Le Bron plays basketball and records the number of free throws he shoots in the first nine games of the season.

Using a 5-number summary of this dataset, or otherwise, determine

  1. the median   (1 mark)

  2. the interquartile range   (2 marks)

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Box Plots and 5-Number, SM-Bank 004

Robert records the total goals scored in each of the first 11 matches of his favourite soccer team.

Using a 5-number summary of this dataset, or otherwise, determine

  1. the range   (1 mark)

  2. the interquartile range   (2 marks)

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Statistics, STD2 S1 SM-Bank 2 MC

A dataset has the following five-number summary.

If the range of the dataset is 8, what is the minimum value of the dataset?

  1.  2
  2.  3
  3.  4
  4.  7
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Statistics, STD2 S1 2017 HSC 1 MC

The box-and-whisker plot for a set of data is shown.
 

What is the median of this set of data?

  1. 15
  2. 20
  3. 30
  4. 35
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Statistics, STD2 S1 2016 HSC 22 MC

The box-and-whisker plots show the results of a History test and a Geography test.
 

In History, 112 students completed the test. The number of students who scored above 30 marks was the same for the History test and the Geography test.

How many students completed the Geography test?

  1. 8
  2. 50
  3. 56
  4. 112
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Statistics, STD2 S1 2016 HSC 19 MC

A soccer referee wrote down the number of goals scored in 9 different games during the season.

The last number has been omitted. The range of the data is 10.

What is the five-number summary for this data set?

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♦ Mean mark 46%.

Statistics, STD2 S1 2015 HSC 6 MC

The times, in minutes, that a large group of students spend on exercise per day are presented in the box‑and‑whisker plot.
 

What percentage of these students spend between 40 minutes and 60 minutes per day on exercise?

  1. 17%
  2. 20%
  3. 25%
  4. 50%
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Statistics, STD2 S1 2005 HSC 22 MC

Two groups of people were surveyed about their weekly wages. The results are shown in the box-and-whisker plots.
 

Which of the following statements is true for the people surveyed?

  1. The same percentage of people in each group earned more than $325 per week.
  2. Approximately 75% of people under 21 years earned less than $350 per week.
  3. Approximately 75% of people 21 years and older earned more than $350 per week.
  4. Approximately 50% of people in each group earned between $325 and $350 per week.
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Statistics, STD2 S1 2008 HSC 10 MC

The marks for a Science test and a Mathematics test are presented in box-and-whisker plots.
 

 Which measure must be the same for both tests?

  1. Mean
  2. Range
  3. Median
  4. Interquartile range
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Statistics, STD2 S1 2010 HSC 27b

The graphs show the distribution of the ages of children in Numbertown in 2000 and 2010.
  

  1. In 2000 there were 1750 children aged 0–18 years.

     

    How many children were aged 12–18 years in 2000?   (1 mark)

  2. The number of children aged 12–18 years is the same in both 2000 and 2010.

     

    How many children aged 0–18 years are there in 2010?    (1 mark)

  3. Identify TWO changes in the distribution of ages between 2000 and 2010. In your answer, refer to measures of location or spread or the shape of the distributions.   (2 marks)

  4. What would be ONE possible implication for government planning, as a consequence of this change in the distribution of ages?   (1 mark)

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♦ Mean mark (i) 45%

 

♦♦ Mean mark (ii) 25%

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iii. 

♦ Mean mark (iii) 35%
MARKER’S COMMENT: A number of students incorrectly identified “positive” skew as “negative” skew here.

iv. 

♦ Mean mark (iv) 46%
MARKER’S COMMENT: Answers should reflect the 1 mark allocation.

Statistics, STD2 S1 2011 HSC 7 MC

A set of data is displayed in this box-and-whisker plot.
 

Which of the following best describes this set of data?

  1. Symmetrical
  2. Positively skewed
  3. Negatively skewed
  4. Normally distributed
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♦ Mean mark 47%.