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Statistics, STD2 S1 2022 HSC 15 MC

The cumulative frequency graph shows the distribution of the number of movie downloads made by 100 people in one month.
 

Which box-plot best represents the same data as displayed in the cumulative frequency graph?
 

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`C`

Show Worked Solution

`text{1st quartile}\ ~~ 3`

`text{Median}\ ~~ 6`

`text{3rd quartile}\ ~~ 7`

`=>C`


♦♦♦ Mean mark 30%.

Statistics, STD2 S1 2016 HSC 27c

The heights of 400 students were measured. The results are displayed in this cumulative frequency polygon.
 

2ug-2016-hsc-q27_2

 
Use the polygon to estimate the interquartile range.  (2 marks)

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`36\ text(cm)`

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`text(See graph for values:)`

♦ Mean mark 46%.

2ug-2016-hsc-q27c-answer

`IQR` `= Q_3 – Q_1`
  `= 172 – 136`
  `= 36\ text(cm)`

Statistics, STD2 S1 2005 HSC 9 MC

A set of data is represented by the cumulative frequency histogram and ogive.
 

2UG-2005-9MC
 

What is the best approximation for the interquartile range for this set of data?

  1.    25
  2.    30
  3.    35
  4.    40
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`C`

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2UG-2005-9MC Answer

`IQR` `= Q3 − Q1`
  `= 80 − 45`
  `= 35`

`=>  C`

Statistics, STD2 S1 2013 HSC 27c

A retailer has collected data on the number of televisions that he sold each week in 2012.

He grouped the data into classes and displayed the data using a cumulative frequency histogram and polygon (ogive).
 

2013 27c

  1. Use the cumulative frequency polygon to determine the interquartile range.  (2 marks)

  2. Oscar said that the retailer sold 300 televisions in 6 of the weeks in 2012.

     

    Is he correct? Give a reason for your answer.   (1 mark)

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  1. `280`
  2. `text(Oscar is not correct because the data is grouped.)`

  3.  

    `text(He could only say that the retailer sold between 250`

  4.  

    `text(and 350 units in 6 of the weeks in 2012.)`

Show Worked Solution

i.  `text(S)text(ince cumulative frequency = 52 at max)`

♦♦♦ Mean mark 13%
COMMENT: Finding median and quartile values from cumulative frequency charts is an important skill that is often examined.

`=> text(Lower quartile at week) = 52/4 = 13`

`text(Lower quartile = 190)\ \ \ \ text{(from graph)}`

`=> text(Upper quartile at week) = 3 xx 13 = 39`

`text(Upper quartile = 470)`

`:.\ text(IQR)`  `= 470` `-190`
  `=280`

 

ii.  `text(Oscar is not correct because the data is grouped.)`

♦♦♦ This question proved a beast, with a mean mark of 1%. Toughest question in the 2013 exam!

`text(He could only say the retailer sold between)`

`text(250 and 350 units in 6 of the weeks in 2012.)`