OCR S1 2014 June — Question 1 7 marks

Exam BoardOCR
ModuleS1 (Statistics 1)
Year2014
SessionJune
Marks7
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicData representation
TypeCalculate range and interquartile range
DifficultyEasy -1.8 This is a straightforward data handling question requiring only basic reading of stem-and-leaf diagrams and calculation of standard summary statistics (median, quartiles, range). These are routine S1 skills with no problem-solving or conceptual challenge—purely mechanical application of learned procedures.
Spec2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread

1 The stem-and-leaf diagram shows the heights, in metres to the nearest 0.1 m , of a random sample of trees of species \(A\).
5
59
614
6559
72334
7566678
8034
85
means 6.4 m
  1. Find the median and interquartile range of the heights.
  2. The heights, in metres to the nearest 0.1 m , of a random sample of trees of species \(B\) are given below. \(\begin{array} { l l l } 7.6 & 5.2 & 8.5 \end{array}\) 5.2
    6.3
    6.3
    6.8
    7.2
    6.7
    7.3
    5.4
    7.5
    7.4
    6.0
    6.7 In the answer book, complete the back-to-back stem-and-leaf diagram.
  3. Make two comparisons between the heights of the two species of tree.

Question 1:
Part (i)
AnswerMarks Guidance
AnswerMarks Guidance
Median \(= 7.45\) (m)B1 cao
\(IQR = 7.75 - 6.7\) or \(77.5 - 67\) or \(77.75 - 66\) or \(7.8 - 6.5\) or \(78 - 65\)M1 These pairs of values only, and subtract
\(= 1.05\) (m); allow 1.175 or 1.18, NOT 1.3A1 allow 10.5 or 11.75 or 11.8 but only if med \(= 74.5\)
Part (ii)
AnswerMarks Guidance
AnswerMarks Guidance
Correct digits in correct leaves, ignore order, allow one omitted or extra or misplaced or incorrect digitB1* Key: e.g. \(8\
Complete correct diagram including order and key and alignmentB1dep Allow \(8\
Part (iii)
AnswerMarks Guidance
AnswerMarks Guidance
One correct comment on sizeB1 A higher overall / A has more taller trees or fewer shorter / A has higher median. NOT "A higher than B". Allow just quoting two medians even if wrong
One correct comment on spread or shapeB1 B more evenly spread or distributed / B has larger range or IQR. NOT any reference to outliers, sample size, individual trees, two comments on size, two comments on spread
# Question 1:

## Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Median $= 7.45$ (m) | B1 | cao |
| $IQR = 7.75 - 6.7$ or $77.5 - 67$ or $77.75 - 66$ or $7.8 - 6.5$ or $78 - 65$ | M1 | These pairs of values only, and subtract |
| $= 1.05$ (m); allow 1.175 or 1.18, NOT 1.3 | A1 | allow 10.5 or 11.75 or 11.8 but only if med $= 74.5$ |

## Part (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Correct digits in correct leaves, ignore order, allow one omitted or extra or misplaced or incorrect digit | B1* | Key: e.g. $8\|6\|4$ means 6.8 (B) and 6.4 (A); allow just $8\|6$ means 6.8; NOT $8\|6$ means 8.6 |
| Complete correct diagram including order and key and alignment | B1dep | Allow $8\|6$ means 68, if consistent with (i); If all digits in correct rows and orders, & correct key, award this mark unless EITHER: a $2^{nd}$ digit in one row clearly aligned with a $3^{rd}$ digit in another OR 1st, 3rd, 4th & 5th rows are very different lengths |

## Part (iii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| One correct comment on size | B1 | A higher overall / A has more taller trees or fewer shorter / A has higher median. NOT "A higher than B". Allow just quoting two medians even if wrong |
| One correct comment on spread or shape | B1 | B more evenly spread or distributed / B has larger range or IQR. NOT any reference to outliers, sample size, individual trees, two comments on size, two comments on spread |

---
1 The stem-and-leaf diagram shows the heights, in metres to the nearest 0.1 m , of a random sample of trees of species $A$.

\begin{center}
\begin{tabular}{ l | l l l l l l l }
5 &  &  &  &  &  &  &  \\
5 & 9 &  &  &  &  &  &  \\
6 & 1 & 4 &  &  &  &  &  \\
6 & 5 & 5 & 9 &  &  &  &  \\
7 & 2 & 3 & 3 & 4 &  &  &  \\
7 & 5 & 6 & 6 & 6 & 7 & 8 &  \\
8 & 0 & 3 & 4 &  &  &  &  \\
8 & 5 &  &  &  &  &  &  \\
 &  &  &  &  &  &  &  \\
 &  &  &  &  &  &  &  \\
\end{tabular}
\end{center} means 6.4 m

(i) Find the median and interquartile range of the heights.\\
(ii) The heights, in metres to the nearest 0.1 m , of a random sample of trees of species $B$ are given below.\\
$\begin{array} { l l l } 7.6 & 5.2 & 8.5 \end{array}$\\
5.2\\
6.3\\
6.3\\
6.8\\
7.2\\
6.7\\
7.3\\
5.4\\
7.5\\
7.4\\
6.0\\
6.7

In the answer book, complete the back-to-back stem-and-leaf diagram.\\
(iii) Make two comparisons between the heights of the two species of tree.

\hfill \mbox{\textit{OCR S1 2014 Q1 [7]}}