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Data Analysis, GEN1 2024 VCAA 7 MC

Fiona plays nine holes of golf each week, and records her score.

Her mean score for all rounds in 2024 is 55.7

In one round, when she recorded a score of 48 , her standardised score was  \(z=-1.75\)

The standard deviation for score in 2024 is

  1. 1.1
  2. 2.3
  3. 4.4
  4. 6.95
Show Answers Only

\(C\)

Show Worked Solution
\(z\) \(=\dfrac{x-\overline{x}}{s_x}\)
\(-1.75\) \(=\dfrac{48-55.7}{s_x}\)
\(s_x\) \(=\dfrac{48-55.7}{-1.75}\)
  \(=4.4\)

  
\(\Rightarrow C\)

Data Analysis, GEN1 2022 VCAA 4 MC

The age, in years, of a sample of 14 possums is displayed in the dot plot below.
 

The mean and the standard deviation of age for this sample of possums are closest to

  1. mean = 4.25    standard deviation = 2.6
  2. mean = 4.8      standard deviation = 2.4
  3. mean = 4.8      standard deviation = 2.5
  4. mean = 4.9      standard deviation = 2.4
  5. mean = 4.9      standard deviation = 2.5
Show Answers Only

\(E\)

Show Worked Solution

\(\text{By calculator:}\) 

\(\text{Sample standard deviation} = 2.525…\)

\(\text{Mean} = 4.928…\)

\(\Rightarrow E\)

CORE, FUR2-NHT 2019 VCAA 1

The table below displays the average sleep time, in hours, for a sample of 19 types of mammals.
 


 

  1. Which of the two variables, type of mammal or average sleep time, is a nominal variable?  (1 mark)
  2. Determine the mean and standard deviation of the variable average sleep time for this sample of mammals.

     

    Write your answers in the boxes provided below.

     

    Round your answer to one decimal place.  (1 mark)
     

         mean = hours                   standard deviation = hours
     

  3. The average sleep time for a human is eight hours.

     

    What percentage of this sample of mammals has an average sleep time that is less than the average sleep time for a human.

     

    Round your answer to one decimal place.  (1 mark)

  4. The sample is increase in size by adding in the average sleep time of the little brown bat.

     

    Its average sleep time is 19.9 hours.

     

    By how many many hours will the range for average sleep time increase when the average sleep time for the little brown bat is added to the sample?  (1 mark)

Show Answers Only
  1. `text(type of mammal)`
  2. `text(mean)= 9.2 \ text(hours)`

     

    `sigma = 4.2 \ text(hours)`

  3. `31.6text(%)`
  4. `5.4 \ text(hours)`
Show Worked Solution

a.    `text(type of mammal is nominal)`

 
b.    `text(mean)= 9.2 \ text(hours) \ \ text{(by CAS)}`

`sigma = 4.2 \ text(hours) \ \ text{(by CAS)}`
 

c.    `text(Percentage)` `= (6)/(19) xx 100`
  `= 0.3157 …`
  `= 31.6text(%)`

 

d.    `text(Range increase)` `= 19.9 – 14.5`
  `= 5.4 \ text(hours)`

CORE, FUR1 2015 VCAA 3 MC

The dot plot below displays the difference between female and male life expectancy, in years, for a sample of 20 countries.
 

CORE, FUR1 2015 VCAA 3 MC
 

The mean (`barx`) and standard deviation (`s`) for this data are

A.   `text(mean)\ = 2.32` `\ \ \ \ \ text(standard deviation)\ = 5.25`
B.   `text(mean)\ = 2.38` `\ \ \ \ \ text(standard deviation)\ = 5.25`
C.   `text(mean)\ = 5.0` `\ \ \ \ \ text(standard deviation)\ = 2.0`
D.   `text(mean)\ = 5.25` `\ \ \ \ \ text(standard deviation)\ = 2.32`
E.   `text(mean)\ = 5.25` `\ \ \ \ \ text(standard deviation)\ = 2.38`
Show Answers Only

`E`

Show Worked Solution

`text(By calculator.)`

`=> E`

CORE, FUR1 2011 VCAA 6-8 MC

When blood pressure is measured, both the systolic (or maximum) pressure and the diastolic (or minimum) pressure are recorded.

Table 1 displays the blood pressure readings, in mmHg, that result from fifteen successive measurements of the same person's blood pressure.
 

core 2011 VCAA 6-8

Part 1

Correct to one decimal place, the mean and standard deviation of this person's systolic blood pressure measurements are respectively

A.   `124.9 and 4.4`

B.   `125.0 and 5.8`

C.   `125.0 and 6.0`

D.   `125.9 and 5.8`

E.   `125.9 and 6.0`

 

Part 2

Using systolic blood pressure (systolic) as the response variable, and diastolic blood pressure (diastolic) as the explanatory variable, a least squares regression line is fitted to the data in Table 1.

The equation of the least squares regression line is closest to

A.   `text(systolic) = 70.3 + 0.790 xx text(diastolic)`

B.   `text(diastolic) = 70.3 + 0.790 xx text(systolic)`

C.   `text(systolic) = 29.3 + 0.330 xx text(diastolic)`

D.   `text(diastolic) = 0.330 + 29.3 xx text(systolic)`

E.   `text(systolic) = 0.790 + 70.3 xx text(diastolic)`

 

Part 3

From the fifteen blood pressure measurements for this person, it can be concluded that the percentage of the variation in systolic blood pressure that is explained by the variation in diastolic blood pressure is closest to

A.   `25.8text(%)`

B.   `50.8text(%)`

C.   `55.4text(%)`

D.   `71.9text(%)`

E.   `79.0text(%)`

Show Answers Only

`text(Part 1:)\ E`

`text(Part 2:)\ A`

`text(Part 3:)\ A`

Show Worked Solution

`text(Part 1)`

`text{By calculator (using sample standard deviation)}`

`text{the results are: }`

`text(Mean = 125.9, std dev = 6.0)`

`=>E`

 

`text(Part 2)`

`text{By calculator (making sure diastolic values are}`

`text{the explanatory or}\ x text{-variable), the regression line}`

`text(can be expressed as follows,)`

`text(systolic) = 70.3 + 0.790 xx text(diastolic)`

`=>A`

 

`text(Part 3)`

`text{By calculator, the regression line (above) should}`

`text(have found) \ \ r^2 = 0.258,\ text(which means that)`

`text(25.8% of the variation in systolic pressure can be)`

`text(explained by variation in diastolic pressure.)`

`=>A`

CORE, FUR1 2008 VCAA 5 MC

A sample of 14 people were asked to indicate the time (in hours) they had spent watching television on the previous night. The results are displayed in the dot plot below.
 

    2008 5
 

Correct to one decimal place, the mean and standard deviation of these times are respectively

A.   `bar x=2.0\ \ \ \ \ s=1.5`

B.   `bar x=2.1\ \ \ \ \ s=1.5`  

C.   `bar x=2.1\ \ \ \ \ s=1.6`

D.   `bar x=2.6\ \ \ \ \ s=1.2`

E.   `bar x=2.6\ \ \ \ \ s=1.3` 

Show Answers Only

`C`

Show Worked Solution

`text(Data points are:)`

`0,0,0,1,1,2,2,2,2,3,3,4,4,5`

`text(By calculator (using sample standard deviation))`

`bar x=2.1,\ \ s=1.6`

`=>  C`

CORE, FUR1 2014 VCAA 3-5 MC

The following table shows the data collected from a sample of seven drivers who entered a supermarket car park. The variables in the table are:

distance – the distance that each driver travelled to the supermarket from their home
 

    • sex – the sex of the driver (female, male)
    • number of children – the number of children in the car
    • type of car – the type of car (sedan, wagon, other)
    • postcode – the postcode of the driver’s home.
       

Part 1

The mean,  `barx`, and the standard deviation, `s_x`, of the variable, distance, are closest to

A.  `barx = 2.5\ \ \ \ \ \ \s_x = 3.3`

B.  `barx = 2.8\ \ \ \ \ \ \s_x = 1.7`

C.  `barx = 2.8\ \ \ \ \ \ \s_x = 1.8`

D.  `barx = 2.9\ \ \ \ \ \ \s_x = 1.7`

E.  `barx = 3.3\ \ \ \ \ \ \s_x = 2.5`

 

Part 2

The number of categorical variables in this data set is

A.  `0`

B.  `1`

C.  `2`

D.  `3`

E.  `4`

 

Part 3

The number of female drivers with three children in the car is

A.  `0`

B.  `1`

C.  `2`

D.  `3`

E.  `4`

 

Show Answers Only

`text(Part 1:) \ C`

`text(Part 2:)\ D`

`text(Part 3:)\ B`

Show Worked Solution

`text(Part 1)`

`text(By calculator)`

`text(Distance)\ \ barx` `=2.8`
`s_x` `≈1.822`

 
`=>C`

 

`text(Part 2)`

♦♦ Mean mark 29%.
MARKER’S NOTE: Postcodes here are categorical variables. Ask yourself “Does it make sense to calculate the mean of this variable?” If the answer is “No”, the variable is categorical.

`text(Categorical variables are sex, type)`

`text(of car, and post code.)`

`=>D`

 

`text(Part 3)`

`text(1 female driver has 3 children.)`

`=>B`