OCR S1 2008 January — Question 8 12 marks

Exam BoardOCR
ModuleS1 (Statistics 1)
Year2008
SessionJanuary
Marks12
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMeasures of Location and Spread
TypeFind median and quartiles from stem-and-leaf diagram
DifficultyEasy -1.3 This is a straightforward S1 question testing basic statistical skills: reading a stem-and-leaf diagram, finding median/quartiles by counting positions, making simple comparisons, and using coding formulas for mean/standard deviation. All parts are routine recall and mechanical calculation with no problem-solving or insight required.
Spec2.02f Measures of average and spread2.02g Calculate mean and standard deviation

8 The stem-and-leaf diagram shows the age in completed years of the members of a sports club. \section*{Male} \begin{table}[h]
\captionsetup{labelformat=empty} \caption{Female}
8876166677889
7655332121334578899
98443323347
5214018
9050
\end{table} Key: 1 | 4 | 0 represents a male aged 41 and a female aged 40.
  1. Find the median and interquartile range for the males.
  2. The median and interquartile range for the females are 27 and 15 respectively. Make two comparisons between the ages of the males and the ages of the females.
  3. The mean age of the males is 30.7 and the mean age of the females is 27.5 , each correct to 1 decimal place. Give one advantage of using the median rather than the mean to compare the ages of the males with the ages of the females. A record was kept of the number of hours, \(X\), spent by each member at the club in a year. The results were summarised by $$n = 49 , \quad \Sigma ( x - 200 ) = 245 , \quad \Sigma ( x - 200 ) ^ { 2 } = 9849 .$$
  4. Calculate the mean and standard deviation of \(X\).

8 The stem-and-leaf diagram shows the age in completed years of the members of a sports club.

\section*{Male}
\begin{table}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Female}
\begin{tabular}{ r l | l }
8876 & 1 & 66677889 \\
76553321 & 2 & 1334578899 \\
98443 & 3 & 23347 \\
521 & 4 & 018 \\
90 & 5 & 0 \\
\end{tabular}
\end{center}
\end{table}

Key: 1 | 4 | 0 represents a male aged 41 and a female aged 40.\\
(i) Find the median and interquartile range for the males.\\
(ii) The median and interquartile range for the females are 27 and 15 respectively. Make two comparisons between the ages of the males and the ages of the females.\\
(iii) The mean age of the males is 30.7 and the mean age of the females is 27.5 , each correct to 1 decimal place. Give one advantage of using the median rather than the mean to compare the ages of the males with the ages of the females.

A record was kept of the number of hours, $X$, spent by each member at the club in a year. The results were summarised by

$$n = 49 , \quad \Sigma ( x - 200 ) = 245 , \quad \Sigma ( x - 200 ) ^ { 2 } = 9849 .$$

(iv) Calculate the mean and standard deviation of $X$.

\hfill \mbox{\textit{OCR S1 2008 Q8 [12]}}