OCR MEI S1 — Question 2

Exam BoardOCR MEI
ModuleS1 (Statistics 1)
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicDiscrete Probability Distributions
TypeCalculate E(X) from constructed distribution
DifficultyEasy -1.2 This is a straightforward data handling question requiring basic statistical calculations (mean, mean squared deviation) and simple algebraic manipulation. The vertical line chart is routine, identifying skewness is observational, and part (iv) involves elementary arithmetic with means. No complex probability theory or problem-solving insight is needed—purely mechanical application of standard S1 techniques.
Spec2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread
2 Every day, George attempts the quiz in a national newspaper. The quiz always consists of 7 questions. In the first 25 days of January, the numbers of questions George answers correctly each day are summarised in the table below.
Number correct123
Frequency123
  1. Draw a vertical line chart to illustrate the data.
  2. State the type of skewness shown by your diagram.
  3. Calculate the mean and the mean squared deviation of the data.
  4. How many correct answers would George need to average over the next 6 days if he is to achieve an average of 5 correct answers for all 31 days of January?
Question 2:
Part (i)
AnswerMarks Guidance
AnswerMark Guidance
Frequency diagram with labelled linear scalesG1 Labelled linear scales
Correct height of linesG1 Height of lines
2
Part (ii)
AnswerMarks Guidance
AnswerMark Guidance
Negative (skewness)B1
1
Part (iii)
AnswerMarks Guidance
AnswerMark Guidance
\(\Sigma fx = 123\) so mean \(= \frac{123}{25} = 4.92\)B1
\(S_{xx} = 681 - \frac{123^2}{25} = 75.84\)M1 For \(S_{xx}\) attempted
\(\text{M.s.d} = \frac{75.84}{25} = 3.034\)A1 FT their 4.92
3
Part (iv)
AnswerMarks Guidance
AnswerMark Guidance
Total for 25 days is 123 and total for 31 days is 155M1 \(31 \times 5 - 25 \times \text{their } 4.92\)
Hence total for next 6 days is 32 and so mean \(= 5.33\)A1 FT their 123
2
TOTAL: 8
# Question 2:

## Part (i)
| Answer | Mark | Guidance |
|--------|------|----------|
| Frequency diagram with labelled linear scales | G1 | Labelled linear scales |
| Correct height of lines | G1 | Height of lines |
| | **2** | |

## Part (ii)
| Answer | Mark | Guidance |
|--------|------|----------|
| Negative (skewness) | B1 | |
| | **1** | |

## Part (iii)
| Answer | Mark | Guidance |
|--------|------|----------|
| $\Sigma fx = 123$ so mean $= \frac{123}{25} = 4.92$ | B1 | |
| $S_{xx} = 681 - \frac{123^2}{25} = 75.84$ | M1 | For $S_{xx}$ attempted |
| $\text{M.s.d} = \frac{75.84}{25} = 3.034$ | A1 | FT their 4.92 |
| | **3** | |

## Part (iv)
| Answer | Mark | Guidance |
|--------|------|----------|
| Total for 25 days is 123 and total for 31 days is 155 | M1 | $31 \times 5 - 25 \times \text{their } 4.92$ |
| Hence total for next 6 days is 32 and so mean $= 5.33$ | A1 | FT their 123 |
| | **2** | |

**TOTAL: 8**

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2 Every day, George attempts the quiz in a national newspaper. The quiz always consists of 7 questions. In the first 25 days of January, the numbers of questions George answers correctly each day are summarised in the table below.

\begin{center}
\begin{tabular}{ | l | l | l | l | l | l | l | l | }
\hline
Number correct & 1 & 2 & 3 &  &  &  &  \\
\hline
Frequency & 1 & 2 & 3 &  &  &  &  \\
\hline
\end{tabular}
\end{center}

(i) Draw a vertical line chart to illustrate the data.\\
(ii) State the type of skewness shown by your diagram.\\
(iii) Calculate the mean and the mean squared deviation of the data.\\
(iv) How many correct answers would George need to average over the next 6 days if he is to achieve an average of 5 correct answers for all 31 days of January?

\hfill \mbox{\textit{OCR MEI S1  Q2}}
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