| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/3 (Pre-U Mathematics Paper 3) |
| Year | 2013 |
| Session | June |
| Marks | 4 |
| Topic | Measures of Location and Spread |
| Type | Calculate statistics from discrete frequency table |
| Difficulty | Easy -1.3 This is a straightforward calculation of mean and standard deviation from a discrete frequency table using standard formulas. It requires only routine application of well-practiced techniques with no problem-solving or conceptual insight, making it easier than average A-level content. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation |
| Number of people | 1 | 2 | 3 | 4 | 5 |
| Number of cars | 48 | 26 | 14 | 10 | 2 |
**Question 1**
$\bar{x} = \frac{192}{100} = 1.92$ — M1, A1
Use of correct formula for mean; may be implied. c.a.o.
$s = \sqrt{\frac{488}{100} - 1.92^2} = \sqrt{1.1936} = 1.09(25...)$ — M1, A1 **[4]**
Use of correct formula for standard deviation; may be implied. c.a.o.
Accept unbiased estimate 1.09(80…)
If no working shown, answer must be correct to 3 sf (or better) to score.
**Total: [4]**1 Pupils at a certain school carried out a survey of traffic passing the school during a two-hour period one morning. One pupil recorded the number of people in each of the first 100 cars. Her results were as follows.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | }
\hline
Number of people & 1 & 2 & 3 & 4 & 5 \\
\hline
Number of cars & 48 & 26 & 14 & 10 & 2 \\
\hline
\end{tabular}
\end{center}
Find the mean and the standard deviation of the number of people per car in her sample.
\hfill \mbox{\textit{Pre-U Pre-U 9794/3 2013 Q1 [4]}}