| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2010 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Compare multiple measures numerically |
| Difficulty | Moderate -0.8 This is a straightforward descriptive statistics question requiring basic calculations (mean, standard deviation) from given data and interpretation of which measure is most appropriate. The dataset is small with an obvious outlier (48), making the conceptual reasoning simple. All techniques are standard S1 content with no problem-solving or novel insight required. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \(\bar{x} = 18.9 \text{ (132/7)}\), \(\text{sd} = 12.3\) | B1, B1 [2] | |
| (ii) median | B1 [1] | |
| (iii) mode inappropriate because it is 10 and this is the lowest value. mean inappropriate because it is affected by the outlier (of 48). | B1, B1 [2] | Sensible reason allow if seen in (ii). Sensible reason allow if seen in (ii) not 'outliers' in plural |
(i) $\bar{x} = 18.9 \text{ (132/7)}$, $\text{sd} = 12.3$ | B1, B1 [2] |
(ii) median | B1 [1] |
(iii) mode inappropriate because it is 10 and this is the lowest value. mean inappropriate because it is affected by the outlier (of 48). | B1, B1 [2] | Sensible reason allow if seen in (ii). Sensible reason allow if seen in (ii) not 'outliers' in plural
---The times in minutes for seven students to become proficient at a new computer game were measured. The results are shown below.
$$15 \quad 10 \quad 48 \quad 10 \quad 19 \quad 14 \quad 16$$
\begin{enumerate}[label=(\roman*)]
\item Find the mean and standard deviation of these times. [2]
\item State which of the mean, median or mode you consider would be most appropriate to use as a measure of central tendency to represent the data in this case. [1]
\item For each of the two measures of average you did not choose in part (ii), give a reason why you consider it inappropriate. [2]
\end{enumerate}
\hfill \mbox{\textit{CAIE S1 2010 Q1 [5]}}