Quartiles
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Either paper 4 marks
The box plot shows information about the times taken by a group of students to solve a puzzle.
(a)State the median time.
(b)Find the range of the times.
(c)Find the interquartile range of the times.
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Either paper 4 marks
The stem-and-leaf diagram shows the number of minutes eleven trains were delayed.
Stem Leaf 2 0 3 6 9 3 1 2 4 7 4 0 3 9 Key: 2 | 0 means 20 minutes
(a)Calculate the median.
(b)Calculate the interquartile range.
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Either paper 3 marks
Here are the marks of 11 students in a test, written in order.
\(1,\ 8,\ 11,\ 17,\ 22,\ 28,\ 31,\ 36,\ 44,\ 48,\ 53\)
(a)State the lower quartile.
(b)State the upper quartile.
(c)Work out the interquartile range.
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Either paper 5 marks
Here are the numbers of goals scored by eleven hockey players last season.
\(13,\ 27,\ 34,\ 20,\ 37,\ 42,\ 23,\ 29,\ 5,\ 10,\ 17\)
(a)Calculate the median.
(b)Calculate the interquartile range.
(c)A box plot is to be drawn for this data.
Write down the five values it needs.
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Either paper 3 marks
A vet writes the masses of the animals treated last month in order, smallest first. There are \(31\) masses in the list.
(a)Write down the position of the median in the list.
(b)Write down the position of the lower quartile.
(c)Write down the position of the upper quartile.
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Either paper 2 marks
The box plot shows information about the marks scored by a class in a science test.
One of the students had a mark of \(30\) marks.
Is that mark in the top 25% of the marks? Explain your answer.
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Either paper 5 marks
Here are the scores of 11 players on Monday.
\(4,\ 11,\ 53,\ 6,\ 21,\ 46,\ 42,\ 37,\ 27,\ 32,\ 16\)
(a)Work out the median of the Monday points.
(b)Work out the interquartile range of the Monday points.
(c)On Tuesday, the median score was \(32\) points and the interquartile range was \(24\) points.
Compare the two sets of points.
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Either paper 4 marks
The times, in minutes, that 11 patients waited to see a doctor are
\(31,\ 25,\ 19,\ 21,\ 17,\ 22,\ 26,\ 12,\ 29,\ 80,\ 14\)
(a)Find the range of the waiting times.
(b)Find the interquartile range of the waiting times.
(c)Which of the range and the interquartile range better describes how spread out the waiting times were? Give a reason for your answer.
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Either paper 4 marks
The box plots show information about the marks scored by the boys and by the girls in a test.
(a)Find the interquartile range of the marks for Boys.
(b)Compare the marks for Boys with the marks for Girls.
Make one comparison about the average and one about the spread.
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Either paper 3 marks
The table shows information about the heights of the plants in a greenhouse. No diagram has been drawn.
Smallest height \(6\) cm Lower quartile \(10\) cm Median \(15\) cm Range \(22\) cm Interquartile range \(13\) cm (a)Calculate the largest height.
(b)Calculate the upper quartile.
(c)A box plot is to be drawn from this information.
Write down, in order, the five values it needs.
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(a) \(27\ \text{minutes}\)
(b) \(32\ \text{minutes}\)
(c) \(11\ \text{minutes}\) -
(a) \(32\ \text{minutes}\)
(b) \(14\ \text{minutes}\) -
(a) \(11\)
(b) \(44\)
(c) \(33\) -
(a) \(23\ \text{goals}\)
(b) \(21\ \text{goals}\)
(c) \(5\), \(13\), \(23\), \(34\), \(42\) -
(a) the 16th value
(b) the 8th value
(c) the 24th value - No
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(a) \(27\)
(b) \(31\)
(c) Tuesday was higher on average — its median of 32 is greater than Monday's median of 27. Tuesday was also more consistent, because its interquartile range of 24 is smaller than Monday's 31. -
(a) \(68\ \text{minutes}\)
(b) \(12\ \text{minutes}\)
(c) The interquartile range, because it uses only the middle half of the data, so the single long wait of 80 minutes does not affect it. -
(a) \(10\ \text{marks}\)
(b) The median for Girls is higher, \(20\) marks against \(17\) marks, so on average the marks for Girls were greater. The interquartile range for Boys is smaller, \(10\) marks against \(14\) marks, so the marks for Boys were more consistent. -
(a) \(28\ \text{cm}\)
(b) \(23\ \text{cm}\)
(c) \(6\), \(10\), \(15\), \(23\), \(28\)
Takes a couple of seconds the first time a sheet is made.