Question 1 - A-Level Maths

CAIE S1 2014 November — Question 1 3 marks

Exam Board	CAIE
Module	S1 (Statistics 1)
Year	2014
Session	November
Marks	3
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Measures of Location and Spread
Type	Calculate statistics from raw data
Difficulty	Easy -1.8 This is a straightforward calculation of mean and variance from a small dataset of 10 numbers using standard formulas. It requires only direct application of basic statistical definitions with no problem-solving, conceptual understanding, or multi-step reasoning—purely mechanical arithmetic that any A-level student should handle routinely.
Spec	2.02f Measures of average and spread 2.02g Calculate mean and standard deviation

1 Find the mean and variance of the following data. $$\begin{array} { l l l l l l l l l l } 5 & - 2 & 12 & 7 & - 3 & 2 & - 6 & 4 & 0 & 8 \end{array}$$

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Answer	Marks	Guidance
$\text{mean} = \frac{(5 + (-2) + 12 + 7 + (-3) + 2 + (-6) + 4 + 0 + 8)}{10} = 2.7$	B1
$\text{var} = \frac{(5^2 + (-2)^2 + \ldots + 8^2)}{10} - 2.7^2 = 35.1 - 2.7^2 = 27.8$	M1 A1	Subst in correct var formula must have $-\text{mean}^2$
3 marks

| $\text{mean} = \frac{(5 + (-2) + 12 + 7 + (-3) + 2 + (-6) + 4 + 0 + 8)}{10} = 2.7$ | B1 | |
| $\text{var} = \frac{(5^2 + (-2)^2 + \ldots + 8^2)}{10} - 2.7^2 = 35.1 - 2.7^2 = 27.8$ | M1 A1 | Subst in correct var formula must have $-\text{mean}^2$ |
| | | 3 marks |

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1 Find the mean and variance of the following data.

$$\begin{array} { l l l l l l l l l l } 
5 & - 2 & 12 & 7 & - 3 & 2 & - 6 & 4 & 0 & 8
\end{array}$$

\hfill \mbox{\textit{CAIE S1 2014 Q1 [3]}}

This paper (7 questions)

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Q1 3 Q2 6 Q3 5 Q4 7 Q5 9 Q6 10 Q7 10

Answer	Marks	Guidance
\(\text{mean} = \frac{(5 + (-2) + 12 + 7 + (-3) + 2 + (-6) + 4 + 0 + 8)}{10} = 2.7\)	B1
\(\text{var} = \frac{(5^2 + (-2)^2 + \ldots + 8^2)}{10} - 2.7^2 = 35.1 - 2.7^2 = 27.8\)	M1 A1	Subst in correct var formula must have \(-\text{mean}^2\)
3 marks