| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2004 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Compare using calculated statistics |
| Difficulty | Easy -1.2 This is a straightforward statistics question requiring basic calculation of mean and standard deviation from a small dataset (8 values), followed by a simple comparison interpretation. The calculations are routine with no conceptual challenges, and the comparison of consistency via standard deviation is a standard textbook exercise requiring only recall of what standard deviation measures. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation |
| Team \(A\) | 150 | 220 | 77 | 30 | 298 | 118 | 160 | 57 |
| Team \(B\) | 166 | 142 | 170 | 93 | 111 | 130 | 148 | 86 |
| Answer | Marks | Guidance |
|---|---|---|
| \(\bar{x}_A = 139\) (138.75) | B1 | For the mean |
| \(\sigma_A = 83.1\) | B1 | For the sd |
| Answer | Marks | Guidance |
|---|---|---|
| Team B, smaller standard deviation | B1 | Independent mark; need the idea of spread |
| B1 dep | SR If team A has a smaller sd then award B1 only for 'team A, smaller sd' |
# Question 1:
## Part (i)
$\bar{x}_A = 139$ (138.75) | B1 | For the mean
$\sigma_A = 83.1$ | B1 | For the sd
**Total: 2**
## Part (ii)
Team B, smaller standard deviation | B1 | Independent mark; need the idea of spread
| B1 dep | SR If team A has a smaller sd then award B1 only for 'team A, smaller sd'
**Total: 2**
---1 Two cricket teams kept records of the number of runs scored by their teams in 8 matches. The scores are shown in the following table.
\begin{center}
\begin{tabular}{ | l | r r r r r r r r | }
\hline
Team $A$ & 150 & 220 & 77 & 30 & 298 & 118 & 160 & 57 \\
\hline
Team $B$ & 166 & 142 & 170 & 93 & 111 & 130 & 148 & 86 \\
\hline
\end{tabular}
\end{center}
(i) Find the mean and standard deviation of the scores for team $A$.
The mean and standard deviation for team $B$ are 130.75 and 29.63 respectively.\\
(ii) State with a reason which team has the more consistent scores.
\hfill \mbox{\textit{CAIE S1 2004 Q1 [4]}}