OCR S1 2008 January — Question 8

Exam BoardOCR
ModuleS1 (Statistics 1)
Year2008
SessionJanuary
TopicMeasures of Location and Spread
TypeFind median and quartiles from stem-and-leaf diagram

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 \(X\).