Find median and quartiles from raw data list

1 Each of a group of 10 boys estimates the length of a piece of string. The estimates, in centimetres, are as follows. $$\begin{array} { l l l l l l l l l l } 37 & 40 & 45 & 38 & 36 & 38 & 42 & 38 & 40 & 39 \end{array}$$

1. Find the mode.
2. Find the median and the interquartile range.

3 A GCSE geography student is investigating a claim that global warming is causing summers in Britain to have more rainfall. He collects rainfall data from a local weather station for 2001 and 2006. The vertical line chart shows the number of days per week on which some rainfall was recorded during the 22 weeks of summer 2001.
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1. Show that the median of the data is 4 , and find the interquartile range.
2. For summer 2006 the median is 3 and the interquartile range is also 3. The student concludes that the data demonstrate that global warming is causing summer rainfall to decrease rather than increase. Is this a valid conclusion from the data? Give two brief reasons to justify your answer.

1 Giles, a keen gardener, rents a council allotment. During early April 2011, he planted 27 seed potatoes. When he harvested his potato crop during the following August, he counted the number of new potatoes that he obtained from each seed potato. He recorded his results as follows.

1. Calculate values for the median and the interquartile range of these data.
2. Advise Giles on how to record his corresponding data for 2012 so that it would then be possible to calculate the mean number of new potatoes per seed potato.

4 The runs scored by a cricketer in 11 innings during the 2006 season were as follows. $$\begin{array} { l l l l l l l l l l l } 47 & 63 & 0 & 28 & 40 & 51 & a & 77 & 0 & 13 & 35 \end{array}$$ The exact value of \(a\) was unknown but it was greater than 100 .

1. Calculate the median and the interquartile range of these 11 values.
2. Give a reason why, for these 11 values:
   1. the mode is not an appropriate measure of average;
   2. the range is not an appropriate measure of spread.

1 The number of matches in each of a sample of 85 boxes is summarised in the table.

1. For these data:
   1. state the modal value;
   2. determine values for the median and the interquartile range.
2. Given that, on investigation, the 2 extreme values in the above table are 227 and 271 :
   1. calculate the range;
   2. calculate estimates of the mean and the standard deviation.
3. For the numbers of matches in the 85 boxes, suggest, with a reason, the most appropriate measure of spread.

1 The weights, in kilograms, of a random sample of 15 items of cabin luggage on an aeroplane were as follows. \section*{\(\begin{array} { l l l l l l l l l l l l l l l } 4.6 & 3.8 & 3.9 & 4.5 & 4.9 & 3.6 & 3.7 & 5.2 & 4.0 & 5.1 & 4.1 & 3.3 & 4.7 & 5.0 & 4.8 \end{array}\)} For these data:

1. find values for the median and the interquartile range;
2. find the value for the range;
3. state why the mode is not an appropriate measure of average.