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Statistics, 2ADV S2 2022 HSC 11

The table shows the types of customer complaints received by an online business in a month.

  1. What are the values of `A` and `B`?  (2 marks)

  2. The data from the table are shown in the following Pareto chart.
     
     
  3. The manager will address 80% of the complaints.
  4. Which types of complaints will the manager address?  (1 mark)

Show Answers Only
  1. `A=160, \ B=96`
  2. `text{Stock shortages and delivery fees.}`
Show Worked Solution

a.   `A=98+62=160`

`text{% Damaged items}\ = 8/200 xx 100 = 4text{%}`

`text{Cumulative % after damaged items = 96%}`

`B = 92+4=96`
 

b.   `text{The right hand side cumulative frequency percentage}`

`text{shows that 80% of all complaints received concern}`

`text{stock shortages and delivery fees.}`

`:.\ text{The manager will address stock shortages and delivery fees.}`

Statistics, STD2 S1 EQ-Bank 4

A high school conducted a survey asking students what their favourite Summer sport was.

The Pareto chart shows the data collected.
 


 

  1. What percentage of students chose Hockey as their favourite Summer sport?  (1 mark)

  2. What percentage of students chose Touch Football as their favourite Summer sport?  (1 mark)

Show Answers Only
  1. `text(2%)`
  2. `text(22%)`
Show Worked Solution

i.   `text(Method 1)`

`text(Percentage who chose hockey)`

`=\ text{cum freq (at hockey column) – cum freq (at tennis column)}` 

`=100-98`

`=2 text(%)`
 

`text(Method 2)`

`text(Column 1 → 180 people = 30%)`

`text(Total surveyed) = 180 -: 0.3 = 600`

`:.\ text(Hockey %)` `=12/600 xx 100`  
  `=2\text(%)`  

 

ii.   `text(Percentage who chose touch football)`

`=\ text{cum freq (at touch football column) – cum freq (at cricket column)}` 

`=76-54`

`=22 text(%)`

Statistics, STD2 S1 EQ-Bank 6

The Pareto chart below shows the data collected from a survey where people were asked to choose their favourite overseas holiday destination.

Using the chart, how many people were surveyed?  (2 marks)
 

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`500`

Show Worked Solution

`text(Percentage of people whose chose NZ)`

`= 80 – 60`

`= 20text(%)`
 

`text(Number of people who chose NZ)`

`= 100`
 

`text(20%)\ xx\ text(Total surveyed = 100)`

`:.\ text(Total surveyed = 500)`

Statistics, STD2 S1 EQ-Bank 5

An island resort surveyed 400 guests by asking them on which continent they lived.

The table below shows the data collected.
 


 

Complete the Pareto chart below to show the data collected.  (3 marks)
 

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Show Worked Solution

`text(% Asia)\ = 168/400=42 text(%)`

`text(% North America)\ = 120/400=30 text(%)`

`text(% Australia)\ = 88/400=22 text(%)`

`text(% Europe)\ = 24/400=6 text(%)`
 

Statistics, STD2 S1 2019 HSC 10 MC

A school collected data related to the reasons given by students for arriving late. The Pareto chart shows the data collected.
 

What percentage of students gave the reason 'Train or bus delay'?

  1. `text(6%)`
  2. `text(15%)`
  3. `text(30%)`
  4. `text(92%)`
Show Answers Only

`A`

Show Worked Solution

`text(Train or bus delay (%))`

♦♦♦ Mean mark 18%.

`= 92 – 86`

`= 6text(%)`

`=> A`