| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2004 |
| Session | June |
| Marks | 19 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Calculate statistics from raw data |
| Difficulty | Easy -1.3 This is a routine S1 statistics question requiring only standard calculations (mean, SD, median, mode, IQR) and construction of a stem-and-leaf diagram from small datasets. All techniques are straightforward applications of formulas with no problem-solving or interpretation challenges beyond basic comparison. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation2.02i Select/critique data presentation |
| 18 | 18 | 17 | 17 |
| 16 | 17 | 16 | 18 |
| 18 | 14 | 17 | 18 |
| 15 | 17 | 18 | 16 |
| 20 | 16 | 18 | 19 |
| 15 | 14 | 14 | 15 |
| 18 | 15 | 16 | 17 |
| 16 | 18 | 15 | 14 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(\bar{x}=\frac{270}{16}=16.875\) | B1 | \(16.875\), \(16\frac{7}{8}\); \(16.9\); \(16.88\) |
| \(\text{sd}=\sqrt{\frac{4578}{16}-16.875^2}\) | M1 | \(\frac{\sum x^2}{16}-\bar{x}^2\) and \(\sqrt{\phantom{x}}\) |
| A1 ft | All correct | |
| \(=1.16592\ldots\) | A1 | AWRT \(1.17\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Mean \(\%\) attendance \(=\frac{16.875}{18}\times 100\ (=93.75)\) | B1 ft | cao (5 marks) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Back-to-back stem and leaf diagram (First \(4\ | 1\) means \(14\); Second \(1\ | 8\) means \(18\)) |
| M1 | Back-to-back S and L (ignore totals) | |
| M1 | Sensible splits of 1; First-correct | |
| A1, A1 | Second-correct (5 marks) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| First: Mode \(=18\), Median \(=17\), IQR \(=2\) | B1 B1 B1 | |
| Second: Mode \(=15\), Median \(=16\), IQR \(=3\) | B1 B1 B1 | (6 marks) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(\text{Median}_S < \text{Median}_F\); \(\text{Mode}_F > \text{Mode}_S\) | B1 B1 B1 | ANY THREE sensible comments |
| Second had larger spread/IQR | ||
| Only 1 student attends all classes in second | ||
| \(\text{Mean\%}_F > \text{Mean\%}_S\) | (3 marks) |
## Question 4:
### Part (a)(i)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\bar{x}=\frac{270}{16}=16.875$ | B1 | $16.875$, $16\frac{7}{8}$; $16.9$; $16.88$ |
| $\text{sd}=\sqrt{\frac{4578}{16}-16.875^2}$ | M1 | $\frac{\sum x^2}{16}-\bar{x}^2$ and $\sqrt{\phantom{x}}$ |
| | A1 ft | All correct |
| $=1.16592\ldots$ | A1 | AWRT $1.17$ |
### Part (a)(ii)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Mean $\%$ attendance $=\frac{16.875}{18}\times 100\ (=93.75)$ | B1 ft | cao **(5 marks)** |
### Part (b)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Back-to-back stem and leaf diagram (First $4\|1$ means $14$; Second $1\|8$ means $18$) | B1 | Both labels and 1 key |
| | M1 | Back-to-back S and L (ignore totals) |
| | M1 | Sensible splits of 1; First-correct |
| | A1, A1 | Second-correct **(5 marks)** |
### Part (c)
| Answer/Working | Marks | Guidance |
|---|---|---|
| First: Mode $=18$, Median $=17$, IQR $=2$ | B1 B1 B1 | |
| Second: Mode $=15$, Median $=16$, IQR $=3$ | B1 B1 B1 | **(6 marks)** |
### Part (d)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\text{Median}_S < \text{Median}_F$; $\text{Mode}_F > \text{Mode}_S$ | B1 B1 B1 | ANY THREE sensible comments |
| Second had larger spread/IQR | | |
| Only 1 student attends all classes in second | | |
| $\text{Mean\%}_F > \text{Mean\%}_S$ | | **(3 marks)** |
**(19 marks total)**
---4. The attendance at college of a group of 18 students was recorded for a 4-week period.
The number of students actually attending each of 16 classes are shown below.
\begin{center}
\begin{tabular}{ l l l l }
18 & 18 & 17 & 17 \\
16 & 17 & 16 & 18 \\
18 & 14 & 17 & 18 \\
15 & 17 & 18 & 16 \\
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Calculate the mean and the standard deviation of the number of students attending these classes.
\item Express the mean as a percentage of the 18 students in the group.
In the same 4-week period, the attendance of a different group of 20, students is shown below.
\begin{center}
\begin{tabular}{ l l l l }
20 & 16 & 18 & 19 \\
15 & 14 & 14 & 15 \\
18 & 15 & 16 & 17 \\
16 & 18 & 15 & 14 \\
\end{tabular}
\end{center}
\end{enumerate}\item Construct a back-to-back stem and leaf diagram to represent the attendance in both groups.
\item Find the mode, median and inter-quartile range for each group of students.
The mean percentage attendance and standard deviation for the second group of students are 81.25 and 1.82 respectively.
\item Compare and contrast the attendance of these 2 groups of students.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 2004 Q4 [19]}}