| Exam Board | Edexcel |
|---|---|
| Module | Paper 3 (Paper 3) |
| Session | Specimen |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Calculate frequency density from frequency |
| Difficulty | Easy -1.3 This is a routine statistics question testing basic histogram mechanics (frequency density calculations), calculator statistics functions, and simple interpretation. Part (a) requires straightforward proportion work with frequency density, parts (b) and (e) are direct calculator/formula applications, and parts (c), (d), (f) involve elementary interpretation with no complex reasoning. All techniques are standard GCSE/AS-level material with no novel problem-solving required. |
| Spec | 2.02b Histogram: area represents frequency2.02f Measures of average and spread2.02g Calculate mean and standard deviation |
| Hours | \(0 \leqslant y < 5\) | \(5 \leqslant y < 8\) | \(8 \leqslant y < 11\) | \(11 \leqslant y < 12\) | \(12 \leqslant y < 14\) |
| Frequency | 12 | 6 | 8 | 3 | 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Clear attempt to relate area to frequency; height × width = 18 | M1 | Can award if their height × their width = 18 |
| height = 7.2 cm | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Correct expression for \(\sigma\) or \(s\) | M1 | Can ft their value for mean |
| awrt 3.69 | A1 | Allow \(s = 3.75\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Suitable comparison of standard deviations to comment on reliability | M1 | |
| Hurn is south of Heathrow and a correct conclusion | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Correct expression using \(\bar{x} + \sigma \approx 10.3\) | M1 | |
| 7 days | A1 | Accept 6 (rounding down) following a correct expression |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Correct probability attempted | M1 | |
| Correct prediction | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Suitable comparison and compatible conclusion | B1 |
# Question 1:
## Part (a)
| Answer | Mark | Guidance |
|--------|------|----------|
| Clear attempt to relate area to frequency; height × width = 18 | M1 | Can award if their height × their width = 18 |
| height = 7.2 cm | A1 | |
## Part (b)
| Answer | Mark | Guidance |
|--------|------|----------|
| Correct expression for $\sigma$ or $s$ | M1 | Can ft their value for mean |
| awrt 3.69 | A1 | Allow $s = 3.75$ |
## Part (c)
| Answer | Mark | Guidance |
|--------|------|----------|
| Suitable comparison of standard deviations to comment on reliability | M1 | |
| Hurn is south of Heathrow and a correct conclusion | A1 | |
## Part (d)
| Answer | Mark | Guidance |
|--------|------|----------|
| Correct expression using $\bar{x} + \sigma \approx 10.3$ | M1 | |
| 7 days | A1 | Accept 6 (rounding down) following a correct expression |
## Part (e)
| Answer | Mark | Guidance |
|--------|------|----------|
| Correct probability attempted | M1 | |
| Correct prediction | A1 | |
## Part (f)
| Answer | Mark | Guidance |
|--------|------|----------|
| Suitable comparison and compatible conclusion | B1 | |
---\begin{enumerate}
\item The number of hours of sunshine each day, $y$, for the month of July at Heathrow are summarised in the table below.
\end{enumerate}
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | }
\hline
Hours & $0 \leqslant y < 5$ & $5 \leqslant y < 8$ & $8 \leqslant y < 11$ & $11 \leqslant y < 12$ & $12 \leqslant y < 14$ \\
\hline
Frequency & 12 & 6 & 8 & 3 & 2 \\
\hline
\end{tabular}
\end{center}
A histogram was drawn to represent these data. The $8 \leqslant y < 11$ group was represented by a bar of width 1.5 cm and height 8 cm .\\
(a) Find the width and the height of the $0 \leqslant y < 5$ group.\\
(b) Use your calculator to estimate the mean and the standard deviation of the number of hours of sunshine each day, for the month of July at Heathrow.\\
Give your answers to 3 significant figures.
The mean and standard deviation for the number of hours of daily sunshine for the same month in Hurn are 5.98 hours and 4.12 hours respectably.\\
Thomas believes that the further south you are the more consistent should be the number of hours of daily sunshine.\\
(c) State, giving a reason, whether or not the calculations in part (b) support Thomas' belief.\\
(d) Estimate the number of days in July at Heathrow where the number of hours of sunshine is more than 1 standard deviation above the mean.
Helen models the number of hours of sunshine each day, for the month of July at Heathrow by $\mathrm { N } \left( 6.6,3.7 ^ { 2 } \right)$.\\
(e) Use Helen's model to predict the number of days in July at Heathrow when the number of hours of sunshine is more than 1 standard deviation above the mean.\\
(f) Use your answers to part (d) and part (e) to comment on the suitability of Helen's model.\\
\hfill \mbox{\textit{Edexcel Paper 3 Q1 [13]}}