| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2019 |
| Session | November |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Identify appropriate measure with outliers |
| Difficulty | Easy -1.2 This is a straightforward descriptive statistics question requiring ordering data to find median and IQR (standard S1 procedure), followed by identifying that the outlier (110) makes the mean inappropriate. Both parts are routine recall and basic calculation with no problem-solving or conceptual depth required. |
| Spec | 2.02f Measures of average and spread |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Median \(= 51\), \(UQ = 57.5\), \(LQ = 40\) | B1 | |
| \(IQR = UQ - LQ\) | M1 | \(55 \leqslant UQ \leqslant 62 - 38 \leqslant LQ \leqslant 45\) |
| \(17.5\) | A1 | NFWW |
| Total: 3 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Result will be disproportionately affected by 110 | B1 | Affected by an extreme/large value; there is a large outlier; ...contains outliers such as 110...; Not 'mean affected by extreme values' |
| Total: 1 |
## Question 1:
### Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Median $= 51$, $UQ = 57.5$, $LQ = 40$ | **B1** | |
| $IQR = UQ - LQ$ | **M1** | $55 \leqslant UQ \leqslant 62 - 38 \leqslant LQ \leqslant 45$ |
| $17.5$ | **A1** | NFWW |
| **Total: 3** | | |
### Part (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Result will be disproportionately affected by 110 | **B1** | Affected by an extreme/large value; there is a large outlier; ...contains outliers such as 110...; Not 'mean affected by extreme values' |
| **Total: 1** | | |
---1 Twelve tourists were asked to estimate the height, in metres, of a new building. Their estimates were as follows.
$$\begin{array} { l l l l l l l l l l l l }
50 & 45 & 62 & 30 & 40 & 55 & 110 & 38 & 52 & 60 & 55 & 40
\end{array}$$
(i) Find the median and the interquartile range for the data.\\
(ii) Give a disadvantage of using the mean as a measure of the central tendency in this case.\\
\hfill \mbox{\textit{CAIE S1 2019 Q1 [4]}}