OCR MEI S1 — Question 4

Exam BoardOCR MEI
ModuleS1 (Statistics 1)
TopicMeasures of Location and Spread
TypeIdentify outliers using IQR rule

4 At a certain stage of a football league season, the numbers of goals scored by a sample of 20 teams in the league were as follows.
\(\begin{array} { l l l l l l l l l l l l l l l l l l l l } 22 & 23 & 23 & 23 & 26 & 28 & 28 & 30 & 31 & 33 & 33 & 34 & 35 & 35 & 36 & 36 & 37 & 46 & 49 & 49 \end{array}\)
  1. Calculate the sample mean and sample variance, \(s ^ { 2 }\), of these data.
  2. The three teams with the most goals appear to be well ahead of the other teams. Determine whether or not any of these three pieces of data may be considered outliers.