Compare multiple measures numerically

1 The times in minutes for seven students to become proficient at a new computer game were measured. The results are shown below. $$\begin{array} { l l l l l l l } 15 & 10 & 48 & 10 & 19 & 14 & 16 \end{array}$$

1. Find the mean and standard deviation of these times.
2. State which of the mean, median or mode you consider would be most appropriate to use as a measure of central tendency to represent the data in this case.
3. For each of the two measures of average you did not choose in part (ii), give a reason why you consider it inappropriate.

1 The total annual emissions of carbon dioxide, \(x\) tonnes per person, for 13 European countries are given below. $$\begin{array} { c c c c c c c c c c c c c } 6.2 & 6.7 & 6.8 & 8.1 & 8.1 & 8.5 & 8.6 & 9.0 & 9.9 & 10.1 & 11.0 & 11.8 & 22.8 \end{array}$$

1. Find the mean, median and midrange of these data.
2. Comment on how useful each of these is as a measure of central tendency for these data, giving a brief reason for each of your answers.

4 A camera records the speeds in miles per hour of 15 vehicles on a motorway. The speeds are given below. $$\begin{array} { l l l l l l l l l l l l l l l } 73 & 67 & 75 & 64 & 52 & 63 & 75 & 81 & 77 & 72 & 68 & 74 & 79 & 72 & 71 \end{array}$$

1. Construct a sorted stem and leaf diagram to represent these data, taking stem values of \(50,60 , \ldots\).
2. Write down the median and midrange of the data.
3. Which of the median and midrange would you recommend to measure the central tendency of the data? Briefly explain your answer.

2 The total annual emissions of carbon dioxide, \(x\) tonnes per person, for 13 European countries are given below.

1. Find the mean, median and midrange of these data.
2. Comment on how useful each of these is as a measure of central tendency for these data, giving a brief reason for each of your answers.

9 The table shows information about the number of days absent last year by students in class 2A at a certain school.

1. Calculate an estimate of the mean for these data.
2. Find the median of these data. The headteacher is writing a report on the numbers of absences at her school. She wishes to include a figure for the average number of absences in class 2A. A governor suggests that she should quote the mean. The class teacher suggests that she should quote the median, because it is lower than the mean.
3. Give another reason for using the median rather than the mean for the average number of absences in class 2A.

5 Fig. 5 shows the number of times that students at a sixth form college visited a recreational mathematics website during the first week of the summer term. \begin{table}[h] \end{table}

1. State the value of the mid-range of the data.
2. Describe the shape of the distribution.
3. State the value of the mode.

5 In a game it is known that:

• 25\% of players score 0
• 30\% of players score 5
• 35\% of players score 10
• 10\% of players score 20

Players receive prize money, in pounds, equal to 100 times their score.
5

1. State the modal score.
   [0pt] [1 mark] 5
2. Find the median score.
   5
3. Find the mean prize money received by a player.