AQA S1 2015 June — Question 1 6 marks

Exam BoardAQA
ModuleS1 (Statistics 1)
Year2015
SessionJune
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicData representation
TypeDraw box plot from raw data
DifficultyEasy -1.2 This is a straightforward S1 question requiring students to calculate five-number summary statistics (minimum, Q1, median, Q3, maximum) from raw data and draw a box plot. It involves standard procedures with no problem-solving or conceptual challenges beyond basic data handling.
Spec2.02f Measures of average and spread2.02g Calculate mean and standard deviation
1 The number of passengers getting off the 11.45 am train at a railway station on each of 35 days is summarised as follows.
Question 1:
Part (a)
AnswerMarks Guidance
AnswerMark Guidance
Mode = 10B1 cao
Cumulative frequencies: 1, 2, 4, 13, 20, 24, 29, 32, 35M1 For attempting cumulative frequencies to find median/quartiles
Median = 18th value = 10A1 cao
\(Q_1\) = 9th value = 10, \(Q_3\) = 27th value = 12M1 For attempting to find both quartiles
IQR = 12 − 10 = 2A1 cao
Part (b)
AnswerMarks Guidance
AnswerMark Guidance
\(\sum fx = 6(1)+7(1)+8(2)+9(9)+10(7)+11(4)+12(5)+...\)M1 Attempt at \(\sum fx / 35\)
\(= 6+7+16+90+70+44+60+45+54 = 392\)
\(\bar{x} = \frac{392}{35} = \mathbf{11.2}\)A1 cao 
# Question 1:

## Part (a)

| Answer | Mark | Guidance |
|--------|------|----------|
| **Mode = 10** | B1 | cao |
| Cumulative frequencies: 1, 2, 4, 13, 20, 24, 29, 32, 35 | M1 | For attempting cumulative frequencies to find median/quartiles |
| **Median = 18th value = 10** | A1 | cao |
| $Q_1$ = 9th value = 10, $Q_3$ = 27th value = 12 | M1 | For attempting to find both quartiles |
| **IQR = 12 − 10 = 2** | A1 | cao |

## Part (b)

| Answer | Mark | Guidance |
|--------|------|----------|
| $\sum fx = 6(1)+7(1)+8(2)+9(9)+10(7)+11(4)+12(5)+...$ | M1 | Attempt at $\sum fx / 35$ |
| $= 6+7+16+90+70+44+60+45+54 = 392$ | | |
| $\bar{x} = \frac{392}{35} = \mathbf{11.2}$ | A1 | cao |

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1 The number of passengers getting off the 11.45 am train at a railway station on each of 35 days is summarised as follows.

\hfill \mbox{\textit{AQA S1 2015 Q1 [6]}}
This paper (7 questions)
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Q1 6 Q2 10 Q3 11 Q4 15 Q5 11 Q6 12 Q7 10