| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/3 (Pre-U Mathematics Paper 3) |
| Year | 2014 |
| Session | June |
| Marks | 5 |
| Topic | Measures of Location and Spread |
| Type | Calculate statistics from grouped frequency table |
| Difficulty | Easy -1.3 This is a straightforward statistics question requiring standard calculations of mean and standard deviation from grouped frequency data using midpoints. It involves routine application of formulas with no conceptual challenges or problem-solving—purely mechanical computation that any A-level student should be able to execute with basic calculator work. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation |
| Mass (\(x\) kg) | \(1.6 \leqslant x < 1.8\) | \(1.8 \leqslant x < 2.0\) | \(2.0 \leqslant x < 2.2\) | \(2.2 \leqslant x < 2.4\) | \(2.4 \leqslant x < 2.6\) |
| Number of chickens | 16 | 27 | 28 | 18 | 11 |
| Answer | Marks | Guidance |
|---|---|---|
| \(\bar{x} = \frac{206.2}{100} = 2.062\) (kg) | M1 A1 | With no working shown allow only correct answers (to 3 s.f. or better). Use of mid-points seen or implied. c.a.o. |
| \(s = \sqrt{\frac{431.16}{100} - 2.062^2}\) | M1 B1 | Use of correct formula for standard deviation; may be implied. Correct \(\Sigma/x^2\) s.o.i. c.a.o. Allow unbiased estimator (0.24568...) for full marks. |
| \(\therefore s = \sqrt{0.059756} = 0.244(45...)\) (kg) | A1 | 2.06 used for sd (gives 0.2607... or unbiased 0.2620...) gets max M1 B1 A0. |
$\bar{x} = \frac{206.2}{100} = 2.062$ (kg) | M1 A1 | With no working shown allow only correct answers (to 3 s.f. or better). Use of mid-points seen or implied. c.a.o.
$s = \sqrt{\frac{431.16}{100} - 2.062^2}$ | M1 B1 | Use of correct formula for standard deviation; may be implied. Correct $\Sigma/x^2$ s.o.i. c.a.o. Allow unbiased estimator (0.24568...) for full marks.
$\therefore s = \sqrt{0.059756} = 0.244(45...)$ (kg) | A1 | 2.06 used for sd (gives 0.2607... or unbiased 0.2620...) gets max M1 B1 A0.The masses, in kilograms, of 100 chickens on sale in a large supermarket were recorded as follows.
\begin{tabular}{|c|c|c|c|c|c|}
\hline
Mass ($x$ kg) & $1.6 \leqslant x < 1.8$ & $1.8 \leqslant x < 2.0$ & $2.0 \leqslant x < 2.2$ & $2.2 \leqslant x < 2.4$ & $2.4 \leqslant x < 2.6$ \\
\hline
Number of chickens & 16 & 27 & 28 & 18 & 11 \\
\hline
\end{tabular}
Calculate estimates of the mean and standard deviation of the masses of these chickens. [5]
\hfill \mbox{\textit{Pre-U Pre-U 9794/3 2014 Q1 [5]}}