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Data Analysis, SM-Bank 038

Jason recorded the following marks out of 100 in his last 8 class tests.
 

74,  65,  70,  72,  95,  68,  70,  64
 

  1. Which one of his marks is an outlier?  (1 mark)

  2. If the outlier is removed, by how many marks does the mean change?  (2 marks)

  3. Explain why it would be more appropriate to use the median rather than the mean when including the outlier in Jason's marks.  (2 marks)

Show Answers Only

a.   `95`

b.   `72.25 \-\69 = 3.25\ text(marks)`

c.   “

Show Worked Solution

a.   `text(The test mark of 95 is significantly different from the other marks)`

`:.\  95\ text(is an outlier)`
 

b.  `text(Initial Mean)`

`text(Mean)` `=(74 + 65 + 70 + 72 + 95 + 68 + 70 + 64)/8`  
  `= 578/8`  
  `= 72.25`  

 
`text(Mean without outlier)`

`text(New Mean)` `=(74 + 65 + 70 + 72  + 68 + 70 + 64)/7`
  `= 483/7`
  `= 69`

`:.\ text(The mean decreases by)\ 3.25\ text(marks)`

c.   `text(Ordered marks):\  64, \ 65, \ 68, \  70, \ 70, \ 72, \ 74, \ 95 `

`:.\ text(When 95 is included, the median is 70 where as the mean is 72.25.)`

`72.25\ text(lies between his 6th and 7th scores and is, therefore, not a)`

`text(good measure of centre for Jason’s marks.)`

Statistics, STD2 S1 2007 HSC 24a

Consider the following set of scores:

`3, \ 5, \ 5, \ 6, \ 8, \ 8, \ 9, \ 10, \ 10, \ 50.` 

  1. Calculate the mean of the set of scores.   (1 mark)

  2. What is the effect on the mean and on the median of removing the outlier?   (2 marks)

Show Answers Only

a.    `11.4`

b.    `text{If the outlier (50) is removed, the mean}`

`text(would become lower.)`

`text(Median will NOT change.)`

Show Worked Solution

a.    `text(Total of scores)`

`= 3 + 5 + 5 + 6 + 8 + 8 + 9 + 10 + 10 +50`

`= 114`

`:.\ text(Mean) = 114/10 = 11.4`
  

b.   `text(Mean)`

`text{If the outlier (50) is removed, the mean}`

`text(would become lower.)`
 

`text(Median)`

`text(The current median (10 data points))`

`= text(5th + 6th)/2 = (8 + 8)/2 = 8`

`text(The new median (9 data points))`

`=\ text(5th value)= 8`

`:.\ text(Median will NOT change.)`