Outliers and cleaning dataEdexcel A-Level Maths: Subtopic test

1. 1
   The numbers of text messages sent in one day by 40 students have minimum 3, lower quartile 14, upper quartile 22 and maximum 50. A value is an outlier if it is more than $1.5\times$IQR above the upper quartile or below the lower quartile.

   (a)

   What is the upper limit above which a value is classed as an outlier?

   [1 mark]

   • A34
   • B23.5
   • C30
   • D44

   (b)

   Which statement about the minimum value 3 and the maximum value 50 is correct?

   [1 mark]

   • ABoth 3 and 50 are outliers
   • BNeither value is an outlier
   • COnly 3 is an outlier
   • DOnly 50 is an outlier

   (c)

   The maximum value of 50 was recorded in error and should have been 15. State what should be done with this value and find the effect on the mean.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   The masses of 200 loaves from a bakery have mean 805 g and standard deviation 6 g. A loaf is classed as an outlier if its mass is more than 3 standard deviations from the mean.

   (a)

   What is the largest mass that is not an outlier?

   [1 mark]

   • A811 g
   • B817 g
   • C823 g
   • D829 g

   (b)

   Which of these masses would be classed as an outlier?

   [1 mark]

   • A788 g
   • B786 g
   • C800 g
   • D822 g

   (c)

   A loaf of mass 842 g is an outlier because the scale was faulty. Find the mean mass of the other 199 loaves.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A student measures the heights, in cm, of 8 plants. The values entered in a spreadsheet are 12.5, 13.1, 12.8, 128, 13.4, 12.9 and 13.0, and the cell for the eighth plant was left blank.

   (a)

   Identify the likely error in the data, explain how you would deal with it, and calculate the mean height of the plants measured, after dealing with it.

   [3 marks]

   (b)

   Describe two ways of dealing with the missing value, and give a disadvantage of each.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   The prices, in £ thousands, of 12 houses sold in one street are 180, 195, 200, 205, 210, 215, 220, 230, 240, 250, 260 and 900. The lower quartile is 202.5 and the upper quartile is 245.

   (a)

   (i) Use the rule "more than $1.5\times$IQR above the upper quartile or below the lower quartile" to test whether 900 and 180 are outliers.
   (ii) Calculate the mean price of all 12 houses and of the 11 houses without 900, and state which better represents a typical price, giving a reason.

   [6 marks]

   (b)

   A student uses the rule "more than 3 standard deviations from the mean".
   (i) The 12 prices have mean 275.4 and standard deviation 189.6. Decide whether 900 is an outlier by this rule.
   (ii) For the 11 prices without 900, the mean is 218.6 and the standard deviation is 23.3. Show that 260 is not an outlier.
   (iii) Explain why the outlier makes this rule less reliable when applied to all 12 prices.

   [6 marks]

   Total for question 4: 12 marks

End of questions