| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2016 |
| Session | June |
| Marks | 7 |
| 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 standard procedures: reading a stem-and-leaf diagram, finding median and quartiles from ordered data (n=20), calculating IQR, and applying the 1.5×IQR outlier rule. All steps are routine recall with no problem-solving or conceptual challenge, making it easier than average but not trivial since it requires careful calculation. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation2.02h Recognize outliers |
| 25 | 0 | ||
| 26 | 0 | 5 | 8 |
| 27 | 7 | 9 | |
| 28 | 1 | 4 | 5 |
| 29 | 0 | 0 | 2 |
| 30 | 7 | 7 | |
| 31 | 6 | ||
| 32 | 0 | 4 | 7 |
| 33 | 3 | 3 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Median \(= 29.0\) | B1 | Condone wrong method |
| \(IQR = 31.8 - 27.8\) | M1 | For either quartile – allow alternative definitions of quartiles |
| \(= 4.0\) | A1 [3] | Do not allow 27.7, 27.9, 31.6, 32.0 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Lower limit \(= 27.8 - 1.5 \times 4.0 = 21.8\) | M1 | Method for either; For use of mean (29.44) and SD (2.516765…) |
| 27.75, 31.9 lead to 21.525 and 38.125 | A1 | FT sensible quartiles and IQR; \(29.44 \pm 2 \times 2.516765\) M1 |
| 27.7, 31.6 lead to 21.85 and 37.45 | Lower Limit \(= 24.4\) A1 | |
| Upper limit \(= 31.8 + 1.5 \times 4.0 = 37.8\) | A1 | FT sensible quartiles and IQR; Upper limit \(= 34.5\) A1 |
| So there are no outliers (at either end of the distribution) | B1 [4] | Dep on at least one A1; Use of median scores 0/4; So no outliers B1 |
# Question 1:
## Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Median $= 29.0$ | B1 | Condone wrong method |
| $IQR = 31.8 - 27.8$ | M1 | For either quartile – allow alternative definitions of quartiles |
| $= 4.0$ | A1 [3] | Do not allow 27.7, 27.9, 31.6, 32.0 |
## Part (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Lower limit $= 27.8 - 1.5 \times 4.0 = 21.8$ | M1 | Method for either; For use of mean (29.44) and SD (2.516765…) |
| 27.75, 31.9 lead to 21.525 and 38.125 | A1 | FT sensible quartiles and IQR; $29.44 \pm 2 \times 2.516765$ M1 |
| 27.7, 31.6 lead to 21.85 and 37.45 | | Lower Limit $= 24.4$ A1 |
| Upper limit $= 31.8 + 1.5 \times 4.0 = 37.8$ | A1 | FT sensible quartiles and IQR; Upper limit $= 34.5$ A1 |
| So there are no outliers (at either end of the distribution) | B1 [4] | Dep on at least one A1; Use of median scores 0/4; So no outliers B1 |
---1 The stem and leaf diagram illustrates the weights in grams of 20 house sparrows.
\begin{center}
\begin{tabular}{ l | l l l }
25 & 0 & & \\
26 & 0 & 5 & 8 \\
27 & 7 & 9 & \\
28 & 1 & 4 & 5 \\
29 & 0 & 0 & 2 \\
30 & 7 & 7 & \\
31 & 6 & & \\
32 & 0 & 4 & 7 \\
33 & 3 & 3 & \\
\end{tabular}
\end{center}
Key: $\quad 27 \quad \mid \quad 7 \quad$ represents 27.7 grams\\
(i) Find the median and interquartile range of the data.\\
(ii) Determine whether there are any outliers.
\hfill \mbox{\textit{OCR MEI S1 2016 Q1 [7]}}