Outliers and data cleaningAQA A-Level Maths: Subtopic test

1. 1
   The daily numbers of visitors to a museum over a period have lower quartile 24 and upper quartile 36. A value is treated as an outlier if it is more than $1.5\times$ the interquartile range above the upper quartile or more than $1.5\times$ the interquartile range below the lower quartile.

   (a)

   Below which value would a daily number of visitors be an outlier?

   [1 mark]

   • A6
   • B18
   • C12
   • D54

   (b)

   Which of these daily numbers of visitors is an outlier?

   [1 mark]

   • A8
   • B52
   • C63
   • D30

   (c)

   The value 63 is found to be a typing error caused by swapping two digits. State the corrected value and explain whether it is still an outlier.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Ten temperature readings, in $^\circ$C, from a sensor have mean 50 and standard deviation 6. One of the readings is 70. A reading is treated as an outlier if it lies more than 2 standard deviations from the mean.

   (a)

   Above which value would a reading be an outlier?

   [1 mark]

   • A56
   • B68
   • C12
   • D62

   (b)

   Which of these readings is not an outlier?

   [1 mark]

   • A37
   • B38.5
   • C63
   • D70

   (c)

   The reading of 70 is confirmed as a sensor fault and removed. Find the mean of the remaining 9 readings.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A supermarket stores the weekly grocery spend, in pounds, of 200 households in a spreadsheet. Six entries are blank, three entries are $-1$ (the till uses this to mean 'card declined') and one entry is 4500. All the other values are between 15 and 310.

   (a)

   For each of the three kinds of problem entry (blank, $-1$, 4500), state how it should be dealt with before the mean spend is calculated, giving a reason.

   [3 marks]

   (b)

   The sum of the 194 non-blank entries is 25 777.
   (i) Calculate their mean.
   (ii) The $-1$ entries are removed and the 4500 is confirmed to be a typing error for 450. Calculate the mean of the 191 remaining entries.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   The ages, in years, of 11 customers at an evening cinema screening are 17, 19, 20, 21, 22, 23, 24, 25, 27, 29 and 71. The lower quartile is 20 and the upper quartile is 27. A value is treated as an outlier if it is more than $1.5\times$ the interquartile range above the upper quartile or more than $1.5\times$ the interquartile range below the lower quartile.

   (a)

   (i) Show that 71 is an outlier.
   (ii) Find the mean age of the 11 customers, and the mean age of the other 10 customers.
   (iii) State, with a reason, whether the mean or the median is the better measure of a typical age.

   [6 marks]

   (b)

   Four more customers are surveyed. Their recorded ages are 25, 31, 2 and a blank entry. The age 2 is a keying error whose true value cannot be found.
   (i) Explain how the blank entry and the entry 2 should be dealt with.
   (ii) The cleaned ages are combined with the original 11. Find the mean age of these 13 customers.
   (iii) Find the median age of the 13 customers and use it to comment on the mean.

   [6 marks]

   Total for question 4: 12 marks

End of questions