SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Statistics, STD1 S1 2023 HSC 13

The graph shows the frequency of scores out of 10 awarded to a museum by visitors.
 

  1. What is the mode of these data?  (1 mark)

  2. Describe TWO features of this graph.  (2 marks)

Show Answers Only

a.    \(\text{Mode = Score with the highest frequency}=9\)
 

b.    \(\text{Features could include any 2 of the following:}\)

  • \(\text{Data is negatively skewed as the mean and median are to the left of the mode}\)
  • \(\text{23 of the 24 scores, or 95.8%, are 5 or above.}\)
  • \(Q_2\text{(Median)}=8\)
  • \(Q_1=7\text{ and }Q_3=9\)
  • \(IQR=Q_1-Q_3=9-7=2\)
  • \(Q_1-1.5\times IQR=7-1.5\times 2=4\ \ \Rightarrow \ \ \text{1 is an outlier}\)
  • \(\text{Mean}=\dfrac{189}{24}=7.875\)
  • \(\text{If the outlier (1) was removed, Mean}=\dfrac{188}{23}=8.174\text{ (2 d.p.)}\)

Show Worked Solution

a.    \(\text{Mode = Score with the highest frequency}=9\)
 

b.    \(\text{Features could include any 2 of the following:}\)

  • \(\text{Data is negatively skewed as the mean and median are to the left of the mode}\)
  • \(\text{23 of the 24 scores, or 95.8%, are 5 or above.}\)
  • \(Q_2\text{(Median)}=8\)
  • \(Q_1=7\text{ and }Q_3=9\)
  • \(IQR=Q_1-Q_3=9-7=2\)
  • \(Q_1-1.5\times IQR=7-1.5\times 2=4\ \ \Rightarrow \ \ \text{1 is an outlier}\)
  • \(\text{Mean}=\dfrac{189}{24}=7.875\)
  • \(\text{If the outlier (1) was removed, Mean}=\dfrac{188}{23}=8.174\text{ (2 d.p.)}\)

♦ Mean mark (a) 47%.
♦♦♦ Mean mark (b) 18%.

Statistics, STD2 S1 2020 HSC 7 MC

Which histogram best represents a dataset that is positively skewed?

 
 
Show Answers Only

`A`

Show Worked Solution

♦♦ Mean mark 32%.

`text(Positive skew occurs when the tail on the)`

`text{histogram is longer on the right-hand}`

`text{(positive) side.}`

`=> \ A`

Statistics, STD2 S1 2008 HSC 26d

The graph shows the predicted population age distribution in Australia in 2008.
 

 

  1. How many females are in the 0–4 age group?  (1 mark)

  2. What is the modal age group?   (1 mark)

  3. How many people are in the 15–19 age group?   (2 marks)

  4. Give ONE reason why there are more people in the 80+ age group than in the 75–79 age group.   (1 mark)

Show Answers Only
  1. `600\ 000`
  2. `35-39`
  3. `1\ 450\ 000`
  4. `text(The 80+ group includes all people over 80)`

  5.  

    `text(and is not restricted by a 5-year limit.)`

Show Worked Solution
i.    `text{# Females (0-4)}` `= 0.6 xx 1\ 000\ 000`
    `= 600\ 000`

 

ii.    `text(Modal age group)\ =` `text(35 – 39)`

 

iii.   `text{# Males (15-19)}` `= 0.75 xx 1\ 000\ 000`
    `= 750\ 000`

 

`text{# Females (15-19)}` `= 0.7 xx 1\ 000\ 000`
  `= 700\ 000`

 

`:.\ text{Total People (15-19)}` `= 750\ 000 + 700\ 000`
  `= 1\ 450\ 000`

 

iv.   `text(The 80+ group includes all people over 80)`
  `text(and is not restricted by a 5-year limit.)`

Statistics, STD2 S1 2011 HSC 11 MC

The sets of data, `X` and `Y`, are displayed in the histograms.

2UG 2011 11

Which of these statements is true?

  1.   `X` has a larger mode and `Y ` has a larger range.
  2.   `X` has a larger mode and the ranges are the same.
  3.   The modes are the same and `Y` has a larger range.
  4.   The modes are the same and the ranges are the same.
Show Answers Only

`B`

Show Worked Solution
♦ Mean mark 47%

`text(Mode of)\ X=9`

`text(Range of)\ X=9-3=6`

`text(Mode of)\ Y=8`

`text(Range of)\ Y=11-5=6`

`:. X\ text(has a larger mode and ranges are the same)`

`=>B`

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`