Averages
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Either paper 2 marks
Here are Aisha's marks in five tests.
\(10,\ 19,\ 13,\ 6,\ 17\)
Find the mean mark.
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Either paper 6 marksThe table shows the number of cakes sold by four children at a school fair.
Child Number of cakes Owen 13 Priya 3 Callum 18 Zara 19 (a)Calculate the median number of cakes.
(b)Calculate the range.
(c)Draw a bar chart on the grid to show the information in the table.
Each square on the vertical axis represents 1 cake.
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Either paper 4 marks
A game is played 40 times.
The vertical line chart shows the winning scores.
(a)Write down the mode.
(b)The game is played again.
Use the chart to estimate the probability that the winning score is \(54\).
(c)Use the chart to estimate the probability that the winning score is \(51\) or more.
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Either paper 3 marks
The list shows the ages, in years, of the seven members of a chess club.
\(13,\ 20,\ 45,\ 13,\ 27,\ 30,\ 38\)
(a)State the median.
(b)State the mode.
(c)Find the range.
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Either paper 3 marks
Here are the marks scored by eight pupils in a test.
\(10,\ 37,\ 68,\ 59,\ 42,\ 51,\ 21,\ 30\)
(a)Find the median.
(b)A ninth value of \(80\) is added to the list.
Find the median of all nine values.
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Either paper 3 marks
Five boxes were weighed, in kilograms. Here are four of the five values.
\(24,\ 15,\ 29,\ 7\)
The fifth value, which is the largest of the five, has been rubbed out.
The range of all five values is \(33\) kg.
(a)Work out the value that has been rubbed out.
(b)Work out the mean of the five values.
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Either paper 3 marks
Here are the marks scored by six pupils in a test.
\(39,\ 53,\ 34,\ 24,\ 50,\ 16\)
Idris says the mean is \(59\).
(a)Without working out the mean, explain how you can tell that Idris is wrong.
(b)Calculate the correct mean.
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Either paper 3 marks
Six trains have their delays, in minutes, listed in order of size. Three of the delays are missing.
\(4, \ ?, \ 6, \ ?, \ 11, \ ?\)
Complete the list of six delays so that the mode is \(4\), the median is \(7.5\) and the range is \(9\).
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Either paper 6 marks
The bar chart shows information about the goals scored in 20 hockey games. Each game has four quarters.
(a)Which quarter was the mode for the away goals? Circle your answer.
1st 2nd 3rd 4th
(b)There were 20 games. Work out the mean number of goals per game, home and away goals together.
(c)In total, how many more home goals were scored than away goals?
(d)Idris says, “More home teams must have won because there were more home goals.”
Is Idris correct? Give a reason for your answer.
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Either paper 2 marks
In one month, the number of hours of exercise taken by 10 people are
\(45,\ 43,\ 56,\ 56,\ 48,\ 52,\ 54,\ 9,\ 50,\ 47\)
Which is the appropriate average to use in this situation? Tick a box.
mean \(\square\) median \(\square\) mode \(\square\)
Give one reason for each of the other two averages as to why they are not appropriate.
- \(13\)
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(a) \(15.5\)
(b) \(16\)
(c) Four bars: Owen to 13, Priya to 3, Callum to 18 and Zara to 19, on a vertical axis numbered 1 to a square(c) -
(a) \(50\)
(b) \(\frac{3}{20}\)
(c) \(\frac{4}{5}\) -
(a) \(27\)
(b) \(13\)
(c) \(32\) -
(a) \(39.5\)
(b) \(42\) -
(a) \(40\ \text{kg}\)
(b) \(23\ \text{kg}\) -
(a) The mean must lie between the smallest value \(16\) and the largest value \(53\), and \(59\) is bigger than the largest, \(53\).
(b) \(36\) - \(4,\ 4,\ 6,\ 9,\ 11,\ 13\)
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(a) 3rd
(b) \(4.25\)
(c) \(7\)
(d) No. The totals only show how many goals were scored, not how many games each team won. For example, one home win by 10 goals and three away wins by 1 goal each would give the home teams 7 more goals in total, yet the away teams would have won more games. - The median. The mean is not appropriate because the extreme value 9 pulls it down to 46. The mode is not appropriate because the only repeated value is the highest value in the list, so the mode is not in the middle of the data.
Takes a couple of seconds the first time a sheet is made.