| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2002 |
| Session | June |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Draw histogram then find median/quartiles from cumulative frequency |
| Difficulty | Moderate -0.3 This is a standard S1 statistics question covering routine histogram drawing (with unequal class widths requiring frequency density), coded mean/SD calculation with given Σfy², and linear interpolation for the median. All techniques are textbook exercises with no novel problem-solving required, though the multi-part nature and coding arithmetic place it slightly below average difficulty overall. |
| Spec | 2.02b Histogram: area represents frequency2.02g Calculate mean and standard deviation2.02i Select/critique data presentation |
| Weight in kg | Frequency |
| 14.6-14.8 | 1 |
| 14.8-18.0 | 0 |
| 18.0-18.5 | 5 |
| 18.5-20.0 | 6 |
| 20.0-20.2 | 22 |
| 20.2-20.4 | 15 |
| 20.4-21.0 | 1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Frequency densities: \(5, 0, 10, 4, 110, 75, 1.7\) | B1 | |
| Graph: scales and labels, shape, correct frequency densities | B1, M1, A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\Sigma fy = 2888.5\) | B1 | |
| \(\text{Mean weight} = 14 + \dfrac{2888.5}{50 \times 10} = 19.777\) accept \(19.78/19.8\) | M1, A1 | |
| \(S_y = \sqrt{\dfrac{171503.75}{50} - \left(\dfrac{2888.5}{50}\right)^2} = 9.62819\ldots\) awrt \(9.63\) | M1, A1 | |
| \(\text{Standard deviation of weight} = \dfrac{9.62819}{10} = 0.96219\ldots\) accept \(0.963/0.96\) | A1ft | Using \(n-1\) gives \(0.9725\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(Q_2 = 20.0 + \dfrac{(25-12)}{22} \times 0.2 = 20.118\ldots\) accept \(20.1/20.12\) | M1, A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Median — data skewed | B1 | |
| Mean — lower value; fewer complaints | B1 |
## Question 6:
### Part (a)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Frequency densities: $5, 0, 10, 4, 110, 75, 1.7$ | B1 | |
| Graph: scales and labels, shape, correct frequency densities | B1, M1, A1 | |
### Part (b)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\Sigma fy = 2888.5$ | B1 | |
| $\text{Mean weight} = 14 + \dfrac{2888.5}{50 \times 10} = 19.777$ accept $19.78/19.8$ | M1, A1 | |
| $S_y = \sqrt{\dfrac{171503.75}{50} - \left(\dfrac{2888.5}{50}\right)^2} = 9.62819\ldots$ awrt $9.63$ | M1, A1 | |
| $\text{Standard deviation of weight} = \dfrac{9.62819}{10} = 0.96219\ldots$ accept $0.963/0.96$ | A1ft | Using $n-1$ gives $0.9725$ |
### Part (c)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $Q_2 = 20.0 + \dfrac{(25-12)}{22} \times 0.2 = 20.118\ldots$ accept $20.1/20.12$ | M1, A1 | |
### Part (d)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Median — data skewed | B1 | |
| Mean — lower value; fewer complaints | B1 | |
---6. The labelling on bags of garden compost indicates that the bags weigh 20 kg . The weights of a random sample of 50 bags are summarised in the table below.
\begin{center}
\begin{tabular}{|l|l|}
\hline
Weight in kg & Frequency \\
\hline
14.6-14.8 & 1 \\
\hline
14.8-18.0 & 0 \\
\hline
18.0-18.5 & 5 \\
\hline
18.5-20.0 & 6 \\
\hline
20.0-20.2 & 22 \\
\hline
20.2-20.4 & 15 \\
\hline
20.4-21.0 & 1 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item On graph paper, draw a histogram of these data.
\item Using the coding $y = 10$ (weight in $\mathrm { kg } - 14$ ), find an estimate for the mean and standard deviation of the weight of a bag of compost.\\[0pt]
[Use $\Sigma f y ^ { 2 } = 171$ 503.75]
\item Using linear interpolation, estimate the median.
The company that produces the bags of compost wants to improve the accuracy of the labelling. The company decides to put the average weight in kg on each bag.
\item Write down which of these averages you would recommend the company to use. Give a reason for your answer.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 2002 Q6 [14]}}