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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
Show Answers Only

`B`

Show Worked Solution

`text{Since the median (155) is closer to the lower quartile (150) and range}`

`text{low (140) than the upper quartile (190) and range high (200), it is}`

`text{positively skewed.}`

`=>B`

♦ Mean mark 47%.

Statistics, STD2 S5 2010 HSC 4 MC

Which of the following frequency histograms shows data that could be normally distributed?
 

Capture1

Capture2 

Show Answers Only

`A`

Show Worked Solution

`text(Normally distributed data have a frequency)`

`text(histogram graph that is shaped like a bell.)`

`=>  A`

Probability, STD2 S2 2012 HSC 26e

The dot plot shows the number of push-ups that 13 members of a fitness class can do in one minute.

2012 26e

  1.  What is the probability that a member selected at random from the class can do more than 38 push-ups in one minute?   (1 mark)

  2.  A new member who can do 32 push-ups in one minute joins the class.

     

    Does the addition of this new member to the class change the probability calculated in part (i)? Justify your answer.    (1 mark)

Show Answers Only
  1. `7/13`
  2. `text{Yes (See Worked Solutions)}`
Show Worked Solution
i.  `P` `= text(# Members > 38 push-ups)/text(Total members)`
  `= 7/13`

 
ii.   `text(Yes.)`

`Ptext{(+ New member)}` `= text(Members > 38 push-ups)/text(Total members)`
  `= 7/14≠ 7/13`
MARKER’S COMMENT: The most successful candidates used the fraction `7/14` in their part (ii) answer rather than relying solely on words.

Statistics, STD2 S1 2012 HSC 26d

Greg needs to conduct a statistical inquiry into how much time people aged 18–25 years have spent accessing social media websites in the last two weeks. He has decided to survey a sample of students from his university.

The process of statistical inquiry includes the following steps, which are NOT in order.
 

2012 26d 

  1. Using the letters A, B, C, D, E and F, list the steps in the most appropriate order for Greg to conduct his statistical inquiry.   (2 marks)

  2. Greg conducts his statistical inquiry.

     

    At which step in the process would he have drawn this graph?    (1 mark) 

2012 26d2

Show Answers Only
  1. `text(B, E, C, F, D, A)`
  2. `text(F)`
Show Worked Solution

i.   `text(B, E, C, F, D, A)`

ii.   `text(F)`

Measurement, STD2 M6 2012 HSC 20 MC

Town `B` is 80 km due north of Town `A` and 59 km from Town `C`.

Town `A` is 31 km from Town `C`.
 

2012 20 mc
 

 What is the bearing of Town `C` from Town `B`?  

  1.   `019^@`
  2.   `122^@` 
  3.   `161^@` 
  4.   `341^@` 
Show Answers Only

`C`

Show Worked Solution
♦ Mean mark 49%

`text(Using the cosine rule:)`

`cos\ /_B` `= (a^2 + c^2 -b^2)/(2ac)`
  `= (59^2 + 80^2 -31^2)/(2 xx 59 xx 80)`
  `= 0.9449…`
`/_B` `= 19^@\  text((nearest degree))`

 

`:.\ text(Bearing of Town C from B) = 180-19= 161^@`

`=>  C`

Probability, STD2 S2 2012 HSC 17 MC

A spinner with different coloured sectors is spun 40 times. The results are recorded in the table.

 What is the relative frequency of obtaining the colour orange? 

  1.    `3/20`  
  2.    `1/5`  
  3.    `6`  
  4.    `8` 
Show Answers Only

`A`

Show Worked Solution
♦♦ Mean mark 34%
COMMENT: Note that relative frequency is the frequency of an event divided by the total frequencies (i.e. the probability).
`text(Total frequency)` `= 40\ text(spins)`
`text(Orange freq.)` `= 40\-(2 + 4 + 6 + 10 +12)`
  `=6`
`:.\ text(Relative freq.)` `= 6/40 = 3/20`

 
`=>  A`

Statistics, STD2 S4 2012 HSC 11 MC

Which of the following relationships would most likely show a negative correlation?

  1. The population of a town and the number of hospitals in that town. 
  2. The hours spent training for a race and the time taken to complete the race. 
  3. The price per litre of petrol and the number of people riding bicycles to work. 
  4. The number of pets per household and the number of computers per household. 
Show Answers Only

\(B\)

Show Worked Solution

\(\text{Increased hours training should reduce the time}\)

\(\text{to complete a race.}\)

\(\Rightarrow B\)

♦ Mean mark 43%.

Financial Maths, STD2 F4 2012 HSC 9 MC

Tracy invests some money for 2 years at 4% per annum, compounded quarterly. 

2012 9 mc

Which figure from the table should Tracy use to calculate the value of her investment at the end of 2 years?

  1.   1.020 
  2.   1.082
  3.   1.083
  4.   1.369
Show Answers Only

`C`

Show Worked Solution
♦♦♦ Mean mark 24%. The lowest MC mean mark in the 2012 exam.
COMMENT: A process to follow: 1-convert the annual rate to the rate per compounding period. 2-calculate the number of compounding periods.

`text(4% annual)`

`=>\ text(4%)/4=text(1% compounded each quarter)`

`=>n=8\ \ \ \ \ \ text{(8 quarters in 2 years)}`

 

`:.\ text{Factor = 1.083   (from table)}`

`=>  C`

Statistics, STD2 S1 2012 HSC 7 MC

The Pi Company has two bakeries. The radar chart displays the monthly sales for the bakeries.
 

2012 7 mc 

  
What was the difference in sales in June between the two bakeries?

  1.   $7.50
  2.   $17.50
  3.   $7500
  4.   $17 500
Show Answers Only

`D`

Show Worked Solution
`text(Bakery 1 Sales in June)` `= $17\ 500`
`text(Bakery 2 Sales in June)` `=$35\ 000`
`:.\ text(Difference in Sales)` `= 35\ 000 \-17\ 500`
  `= 17\ 500`

`=>  D`

Statistics, STD2 S1 2010 HSC 1 MC

The results of a survey are displayed in the dot plot.

What is the range of this data?
 

2010 1 MC 
 

  1.    7
  2.    8
  3.    9
  4.    10
Show Answers Only

`C`

Show Worked Solution
`text(Range)` `=text(High)-text(Low)`
  `=9-0`
  `=9`

`=>  C`

Statistics, STD2 S1 2012 HSC 1 MC

A set of 15 scores is displayed in a stem-and-leaf plot.
 

2012 1 mc 
 

 What is the median of these scores?

  1.    7 
  2.    8
  3.   77
  4.   78
Show Answers Only

`D`

Show Worked Solution

`text(15 scores)\ \ =>\ \ text(Median is 8th)`

`:.\ \ text(Median is)\ \ 78`

`=>  D`

Statistics, STD2 S5 2013 HSC 20 MC

There are  60 000  students sitting a state-wide examination. If the results form a normal distribution, how many students would be expected to score a result between 1 and 2 standard deviations above the mean?

You may assume for normally distributed data that:

    • 68% of scores have  `z`-scores between  – 1 and 1
    • 95% of scores have  `z`-scores between  – 2 and 2
    • 99.7% of scores have  `z`-scores between  – 3 and 3.
  1. `8100`
  2. `16\ 200`
  3. `20\ 400`
  4. `28\ 500`
Show Answers Only

`A`

Show Worked Solution
♦♦ Mean mark 24% 

`text(S)text(ince 68% between)\ z=1\ text(and)\ -1`

`  =>  text(34% between)\  z=0\ text(and)\   1`

`text(Likewise, 95% between)\ z=2\ text(and)  -2`

`  =>  text(47.5% between)\ z=0\ text(and)\ 2`
 

`:.\ text(% between)\ z=1\ text(and)\ 2`

`=47.5-34`

`=13.5 text(%)`

 
`:.\ text(Students between)\ \ z=1\  text(and)\ \ z=2`

`=13.5 text(%)xx60\ 000`

`=8100`

`=>\ A`

Statistics, STD2 S1 2013 HSC 15 MC

The frequency histogram shows the number of goals scored by a football team in each game in a season.
 

2013 15 mc

 
What is the mean number of goals scored per game by this team?

  1.    4
  2.    4.5
  3.    5
  4.    5.5
Show Answers Only

`C`

Show Worked Solution

`text(Total number of goals scored)`

`=(3xx3)+(4xx7)+(5xx5)+(6xx1)+(7xx0)+(8xx4)`

`=9+28+25+6+0+32`

`=100`

`text(Number of games)=3+7+5+1+4=20`

`:.\ text(Mean goals per game)=100/20=5`

`=>\ C`

Statistics, STD2 S1 2013 HSC 14 MC

The July sales prices for properties in a suburb were:

$552 000,  $595 000,  $607 000,  $607 000,  $682 000, and  $685 000.

On 1 August, another property in the same suburb was sold for over one million dollars.

If the property had been sold in July, what effect would it have had on the mean and median sale prices for July?

  1.    Both the mean and median would have changed.
  2.    Neither the mean nor the median would have changed.
  3.    The mean would have changed and the median would have stayed the same.
  4.    The mean would have stayed the same and the median would have changed.
Show Answers Only

`C`

Show Worked Solution

`text(Mean increases because new house is sold above)`

`text(the existing average.)`

`text(Initial median)= (607\ 000+607\ 000)/2=607\ 000` 

`text(New median)=607\ 000\ \ \  text{(4th value in a list of 7)}`

`=>\ C`

Probability, STD2 S2 2013 HSC 10 MC

Students studying vocational education courses were surveyed about their living arrangements.

One of these students is selected at random.

 What is the probability that this student is male and living with his parent(s)?

  1. 31%
  2. 40%
  3. 56%
  4. 77%
Show Answers Only

`A`

Show Worked Solution

`text(Number of males living with their parents is = 155)`.

`:.\ P=155/505=0.30693…%`

`=>\ A`

Statistics, STD2 S1 2013 HSC 8 MC

A high school has 100 students in each year group, Year 7 to Year 12. A survey is to be conducted to determine the average number of text messages sent per month by students at the school.

Which of the following would provide the most representative sample for this survey?

  1. All Year 7 students
  2. All physics students in Year 11 and 12
  3. 20 students chosen at random from each year group
  4. 120 students chosen at random from the school roll
Show Answers Only

`C`

Show Worked Solution

`text(The best sample would have an equal amount)`

`text(of people in each year randomly selected.)`

`=>\ C`

Probability, STD2 S2 2013 HSC 7 MC

In an experiment, a standard six-sided die was rolled 72 times. The results are shown in the table.
 

Which number on the die was obtained the expected number of times?

  1.    1
  2.    2
  3.    3
  4.    6
Show Answers Only

`B`

Show Worked Solution

`text(Probability of rolling a specific number)=1/6`

`:.\ text(After 72 rolls, a specific number is expected)`

 `1/6xx72=12\ text(times.)`

`=>\ B`

Statistics, STD2 S1 2013 HSC 6 MC

A survey was conducted where people were asked which of two brands of smartphones they preferred. The results were:

  • 48% preferred Brand X
  • 52% preferred Brand Y

A graph displaying the data is to be included in a magazine article. The editor of the magazine wishes to ensure that the graph is not misleading in any way.

Which graph should the editor choose to include in the article?
 

2013 6 mc1

2013 6 mc2

Show Answers Only

`D`

Show Worked Solution

`D\ text(is the best as it starts at zero on the)\ y text(-axis)`

`text(and has the same column widths.)`

Statistics, STD2 S4 2013 HSC 2 MC

Which graph best shows data with a correlation closest to 0.3?
 

2013 2 mc1

2013 2 mc2

 

Show Answers Only

`A`

Show Worked Solution

`A\ text(is correct since the data slopes bottom)`

`text{left to top right (i.e. it’s positive).}`

`D\ text(also slopes correctly but exhibits a higher)`

`text(correlation co-efficient.)`

`=>A`