FURTHER MATHEMATICS 2016

UNIT 3 SAC – DATA ANALYSIS (CORE)

Session #1

Allocation of marks
Session 1 (80 minutes) / 40
Session 2 (100 minutes) / 40

Instructions:

  • You may use one bound reference book that adheres to the VCAA specifications for all three sessions.
  • You may use one CAS calculator, and if desired, one scientific calculator for all three sessions.

TOTAL: ____ + ____ /80 = %

StudentsareNOTpermittedto bringmobilephonesand/orany otherunauthorisedelectroniccommunicationdevicesintotheroomforthistask.

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Question1

Thefollowingdatarepresentaveragefruitweight(grams)of applespertreeforarandom sampleof 28treesinanagriculturalexperiment.

85.3 / 113.8 / 92.9 / 48.9 / 94.4 / 79.1 / 70
86.9 / 87.7 / 67.3 / 117.5 / 98.9 / 108.5 / 104.4
96.8 / 94.5 / 90.6 / 100.8 / 96 / 84.6 / 127.1
108.5 / 99.9 / 129.8 / 94.5 / 99.4 / 117.5 / 135

a. Findthemean,medianandmodeoftheabovedata.Writethevaluescorrecttotwo decimalplaces.

3 marks

b. Whatpercentage,correcttotwodecimalplaces,of treeshadaveragefruitweight(ingrams)

morethan95g?

2 marks

c. Drawahistogramon CAS(use a bin width of 10 and a starting value of 40)anddescribethedistributionofthedata.

2 marks

d. Whichstatisticalmeasureof centreismorereliableforthisdatasetandwhy?

2 marks

1

e. Writedown thefive-numbersummarystatisticsanddecide if there are any outliers and list any that do exist. Show all working out.

4 marks

f.i) Drawaboxplotusingthefive-numbersummarystatisticsfound inparte.

1 mark

ii) Using the boxplot above, describe the distribution of the average fruit weight of apples per tree.

2 marks

g. i) Findthestandarddeviationofthisdatasetcorrecttothreedecimalplacesanduse itto findthestandardizedaveragefruitweightof atreewithanaveragefruitweightof129.8g.

2 marks

ii) Interpret the standardized score found in (i)

1 mark

Another set of data of average fruit weight of apples per tree is normally distributed with a mean weight of 95.5g and a standard deviation of 19.8g.

h. i)What percentage of trees have an average fruit weight greater than 75.7g?

1 marks

ii) What percentage of trees have an average fruit weight between 55.9g and 115.3g?

1 mark

Total21 marks

Question2

Thefollowingtablegivesthemedianage,inyears,of peopleinacountryovertheperiod

1996 -2009.

Year / Median Age
1996 / 40.64
1997 / 41.00
1998 / 41.30
1999 / 39.87
2000 / 38.54
2001 / 36.78
2002 / 36.54
2003 / 36.43
2004 / 33.81
2005 / 34.12
2006 / 32.46
2007 / 32.74
2008 / 30.76
2009 / 29.69

a. Complete the scatterplot below by plotting the bold data values given in the table above. Mark the point with a cross (. Note: Let 1996 = 1, 1997 =2 and so on.

1 mark

b.Use the scatterplot to describe the association between median age and year in terms of strength, direction and form.

2 marks

1

c. Writedown the equationoftheleastsquaresregressionline,intermsofthevariables,with coefficientscorrecttothreesignificant figures.

2 marks

d. Interpret the slope in terms of the variables median age and year

1 mark

e. Writedown thecorrelationcoefficient,correcttofour decimal places and interpret.

2 marks

f. Findthecoefficientof determination correct to four significant figures.Interpret this value in terms of the variables.

2 marks

g. Sketchtheleastsquaresregressionlineontheabovescatterplot.

1marks

h.Using the regression line, findthepredictedvalueofmedianageintheyear2004.

1 mark

Total12marks

Question 3

Those households that use town water and tank water are classified as having small, medium or large tank capacity.

The box plots below show the distribution of the average daily town water consumption (in L) of these three groups of households.

a.What is the inter-quartile range of the distribution of town water consumption for those households with a medium tank capacity?

1 mark

b.Complete the following statement:

The bottom 25% of households with large tank capacity have an average daily town

water consumption of between L and L per day.

1 mark

c.For the three parallel box plots shown above, there appears to be an association between the variables tank capacity and town water consumption.

Using an appropriate statistic, describe the nature of this association.

1 mark

Total3 marks

Question 4

The distribution of sleep duration among children aged 10 to 15 years is shown in the segmented bar chart below.

  1. Complete the following statement:

Segmented bar charts are appropriate to use here as we are investigating the relationship between variables. Another suitable graph that could be used to display this distribution is .

1 mark

  1. What percentage of 13 year olds slept from 9 to 10 hours?

1 mark

  1. Does the graph support the theory that time is related to age? Quote percentages to support your statement.

2 marks

Total 4 marks

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