Identify outliers using mean and standard deviation

Question asks to show a value is an outlier using a criterion based on mean ± k×standard deviation (typically k=2 or k=3), not the IQR rule.

3 questions

OCR MEI S1 2007 June Q3
3 The marks \(x\) scored by a sample of 56 students in an examination are summarised by $$n = 56 , \quad \Sigma x = 3026 , \quad \Sigma x ^ { 2 } = 178890 .$$
  1. Calculate the mean and standard deviation of the marks.
  2. The highest mark scored by any of the 56 students in the examination was 93 . Show that this result may be considered to be an outlier.
  3. The formula \(y = 1.2 x - 10\) is used to scale the marks. Find the mean and standard deviation of the scaled marks.
OCR MEI S1 Q2
2 The marks \(x\) scored by a sample of 56 students in an examination are summarised by $$n = 56 , \quad \Sigma x = 3026 , \quad \Sigma x ^ { 2 } = 178890 .$$
  1. Calculate the mean and standard deviation of the marks.
  2. The highest mark scored by any of the 56 students in the examination was 93. Show that this result may be considered to be an outlier.
  3. The formula \(y = 1.2 x - 10\) is used to scale the marks. Find the mean and standard deviation of the scaled marks.
AQA Paper 3 2019 June Q12
12 Amelia decides to analyse the heights of members of her school rowing club. The heights of a random sample of 10 rowers are shown in the table below.
RowerJessNellLivNeveAnnToriMayaKathDarcyJen
Height (cm)162169172156146161159164157160
12
  1. Any value more than 2 standard deviations from the mean may be regarded as an outlier. Verify that Ann's height is an outlier.
    Fully justify your answer.
    12
  2. Amelia thinks she may have written down Ann's height incorrectly. If Ann's height were discarded, state with a reason what, if any, difference this would make to the mean and standard deviation.