| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2005 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Identify outliers using IQR rule |
| Difficulty | Moderate -0.8 This is a straightforward application of the IQR outlier rule (Q3 + 1.5×IQR) with clearly ordered data. Part (i) requires basic mean and variance calculations, while part (ii) is a standard textbook procedure requiring quartile identification and arithmetic. No conceptual difficulty or problem-solving insight needed. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation2.02h Recognize outliers |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Mean \(= 657/20 = 32.85\) | B1 cao | |
| Variance \(= \frac{1}{19}(22839 - \frac{657^2}{20}) = 66.13\) | M1 A1 cao |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Standard deviation \(= 8.13\) | M1 ft | |
| \(32.85 + 2(8.13) = 49.11\) | A1 ft | Calculation of 49.11 |
| None of the 3 values exceed this so no outliers |
## Question 1:
### Part (i)
| Answer | Mark | Guidance |
|--------|------|----------|
| Mean $= 657/20 = 32.85$ | B1 cao | |
| Variance $= \frac{1}{19}(22839 - \frac{657^2}{20}) = 66.13$ | M1 A1 cao | |
### Part (ii)
| Answer | Mark | Guidance |
|--------|------|----------|
| Standard deviation $= 8.13$ | M1 ft | |
| $32.85 + 2(8.13) = 49.11$ | A1 ft | Calculation of 49.11 |
| None of the 3 values exceed this so no outliers | | |
---1 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.\\
$\begin{array} { l l l l l l l l l l l l l l l l l l l l l } 22 & 23 & 23 & 23 & 26 & 28 & 28 & 30 & 31 & 33 & 33 & 34 & 35 & 35 & 36 & 36 & 37 & 46 & 49 & 49 \end{array}$\\
(i) Calculate the sample mean and sample variance, $s ^ { 2 }$, of these data.\\
(ii) 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.
\hfill \mbox{\textit{OCR MEI S1 2005 Q1 [5]}}