Moderate -0.8 This is a straightforward statistics question requiring only direct application of standard formulas: mean = Σx/n and standard deviation = √(Σx²/n - μ²). Part (c) asks for a basic comparison of two sets of summary statistics with no deeper analysis required. All three parts are routine calculations with no problem-solving or conceptual challenge beyond A-level basics.
The annual cost of energy in 2021 for each of the 350 households in Village A can be modelled by a random variable \(X\)
It is given that
$$\sum x = 945\,000 \quad \sum x^2 = 2\,607\,500\,000$$
\begin{enumerate}[label=(\alph*)]
\item Calculate the mean of \(X\).
[1 mark]
\item Calculate the standard deviation of \(X\).
[2 marks]
\item For households in Village B the annual cost of energy in 2021 has mean £3100 and standard deviation £325
Compare the annual cost of energy in 2021 for households in Village A and Village B.
[2 marks]
Question 14:
--- 14(a) ---
14(a) | Obtains 2700 | 1.1b | B1 | 2700
Subtotal | 1
Q | Marking instructions | AO | Marks | Typical solution
--- 14(b) ---
14(b) | Uses the correct formula for
standard deviation using their
mean
PI by 400 | 1.1a | M1 | 2 6 0 7 5 0 0 0 0 0
− 2 7 0 0 2 = 400
3 5 0
Obtains 400 | 1.1b | A1
Subtotal | 2
Q | Marking instructions | AO | Marks | Typical solution
--- 14(c) ---
14(c) | Concludes correctly in context
for the means
Comparison must include the
word such as ‘on average’ or
‘typically’ etc
Follow through the correct
comparison of 3100 with their
mean from part 14(a) | 2.4 | E1F | The cost of energy for households
in Village A is less on average
The variation in cost of energy is
higher in Village A.
Concludes correctly in context
for the standard deviations
Comparison must include the
word such as ‘varies’, ‘spread’
‘disperse’ ‘variation’ or
‘consistent’ etc
Follow through the correct
comparison of 325 with their
standard deviation from part
14(b)
Do not allow comparison that
includes ‘range’ or ‘variety’ | 2.4 | E1F
Subtotal | 2
Question 14 Total | 5
Q | Marking instructions | AO | Marks | Typical solution
The annual cost of energy in 2021 for each of the 350 households in Village A can be modelled by a random variable $X$
It is given that
$$\sum x = 945\,000 \quad \sum x^2 = 2\,607\,500\,000$$
\begin{enumerate}[label=(\alph*)]
\item Calculate the mean of $X$.
[1 mark]
\item Calculate the standard deviation of $X$.
[2 marks]
\item For households in Village B the annual cost of energy in 2021 has mean £3100 and standard deviation £325
Compare the annual cost of energy in 2021 for households in Village A and Village B.
[2 marks]
</end{enumerate}
\hfill \mbox{\textit{AQA Paper 3 2024 Q14 [5]}}