OCR MEI S1 (Statistics 1)

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.

3 Every day, George attempts the quiz in a national newspaper. The quiz always consists of 7 questions. In the first 25 days of January, the numbers of questions George answers correctly each day are summarised in the table below.

1. On the insert, draw a cumulative frequency diagram to illustrate the data.
2. Use your graph to estimate the median length of journey and the quartiles. Hence find the interquartile range.
3. State the type of skewness of the distribution of the data.

4 Answer part (i) of this question on the insert provided. A taxi driver operates from a taxi rank at a main railway station in London. During one particular week he makes 120 journeys, the lengths of which are summarised in the table.

1. On the insert, draw a cumulative frequency diagram to illustrate the data.
2. Use your graph to estimate the median length of journey and the quartiles. Hence find the interquartile range.
3. State the type of skewness of the distribution of the data.

5 A pear grower collects a random sample of 120 pears from his orchard. The histogram below shows the lengths, in mm , of these pears.
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1. Calculate the number of pears which are between 90 and 100 mm long.
2. Calculate an estimate of the mean length of the pears. Explain why your answer is only an estimate.
3. Calculate an estimate of the standard deviation.
4. Use your answers to parts (ii) and (iii) to investigate whether there are any outliers.
5. Name the type of skewness of the distribution.
6. Illustrate the data using a cumulative frequency diagram.

6 The times taken for 480 university students to travel from their accommodation to lectures are summarised below.

1. Illustrate these data by means of a histogram.
2. Identify the type of skewness of the distribution.