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KS3 Maths · Year 7Chapter 13 · Statistics
Year 7 · Chapter 13

Statistics

By the end of this chapter you will be able to

  • Tell categorical from numerical data, and discrete from continuous data
  • Read and draw frequency tables, bar charts, pictograms and line graphs
  • Find the mean, median, mode and range of a list, and of a frequency table
  • Estimate the mean of grouped data using the midpoints of the groups
  • Describe the correlation in a scatter graph, and use a line of best fit to estimate a value
  • Compare two sets of data using an average and the spread

You should already know

  • Ordering numbers, tally charts and frequency tables (Year 6, Chapter 13)
  • Mean as sharing equally, and the fraction and percentage ideas from Chapter 2
  • Coordinates and graphs (Chapter 7)

Where this leads

  • Cumulative frequency, box plots and histograms in Year 8
  • Standard deviation and more complex statistical models in Years 8 and 9

National Curriculum for England, Key Stage 3 mathematics, Year 7. Content: S1 describe, interpret and compare distributions of one variable with suitable graphs, and measures of average and spread (mean, median, mode, range), S2 construct and interpret tables, charts and diagrams for categorical data, and bar and line charts for numerical data, ungrouped or grouped, S3 describe simple relationships between two variables (bivariate data) and illustrate them with a scatter graph.

Exercise P  Do you remember?

Non-calculator
1
FWork out 15 ÷ 3.
2
FPut these in order from smallest: 4, 9, 1, 7.
3
FWhat is the total of 6, 8 and 10?
4
FWhat is the middle number of 3, 5 and 9?
5
FWhat is 7 + 9 + 4?
13.1

Types of data and frequency tables

Year 7
S2
Video lesson: Types of data and frequency tablesComing soon
A class surveys its favourite fruit, the number of brothers and sisters of each pupil, and their heights. The first is a word, the second is a whole number that is counted, and the third is a measurement. Each needs a different kind of chart.

Categorical data is in groups described by words, such as favourite colour. Numerical data is a number: discrete numerical data is counted in whole steps (such as shoe size), and continuous numerical data is measured (such as height in cm).

A frequency table lists each value (or group) and how many times it occurs. The total frequency is the sum of all the frequencies.

Key ideas

  • Categorical: groups described in words, such as colour or pet.
  • Discrete numerical: counted in whole numbers, such as the number of goals.
  • Continuous numerical: measured, such as height or time.
  • Total frequency = the sum of all the frequencies.
Worked example 13.1.1
Shoe sizes of six pupils: 6, 7, 6, 8, 7, 6. Make a frequency table.

Method. Count how many pupils have each size.

  1. Count the 6s. Three pupils have size 6.
    6: 3
  2. Count the 7s and 8s. Two pupils have size 7 and one has size 8.
    7: 2, 8: 1
  3. Write the answer. Give the answer with its unit.
    Size 6: 3, size 7: 2, size 8: 1

Check. 3 + 2 + 1 = 6 pupils. ✓

Watch out. Check the total of the frequencies is 6.

Worked example 13.1.2
Is "height in cm" categorical, discrete or continuous?

Method. Height is measured, not counted.

  1. Read the data. Write down the values before working out the statistic.
    measured
  2. Decide the type. Height is a number that can take any value in a range.
    measured
  3. Write the answer. Give the answer with its unit.
    numerical and continuous

Check. Height can be 150.5 cm, so it is continuous. ✓

Watch out. Measured quantities are continuous.

Worked example 13.1.3
Is "number of brothers" categorical, discrete or continuous?

Method. The number of brothers is counted.

  1. Read the data. Write down the values before working out the statistic.
    counted
  2. Decide the type. It is a count of whole people, in steps of 1.
    counted
  3. Write the answer. Give the answer with its unit.
    numerical and discrete

Check. You cannot have 2.5 brothers. ✓

Watch out. Counts are discrete.

Watch out

Watch out: shoe size is not continuous, because sizes go up in steps (such as 6, 6.5, 7). A discrete quantity has gaps between values.

Exam tip

Grown-up tip. Ask the pupil to make a tally of the colours of the cars passing the window for two minutes.

Exercise 13A  Data types and frequency tables

Non-calculator
1
FIs "favourite colour" categorical or numerical?
2
FIs "number of brothers" discrete or continuous?
3
FIs "height in cm" discrete or continuous?
4
FShoe sizes: 6, 7, 6, 8, 7, 6. How many pupils have size 6?
5
FA frequency table has frequencies 4, 7, 3 and 6. Find the total frequency.
6
FVotes: A, B, A, C, B, A, A. How many votes did A get?
7
PSA table has values 1, 2 and 3 with frequencies 5, a missing frequency, and 4. The total frequency is 14. Find the missing frequency.
8
FFive red, eight blue and three green counters are counted. Which colour is most common?
9
PS30 pupils are asked for their favourite fruit: 12 apples, 10 pears, 8 bananas. How many did not choose apples?
10
FClassify each: (a) age in years (b) mass in kg (c) favourite pet
(a)(a) age in years
(b)(b) mass in kg
(c)(c) favourite pet
11
RSam says shoe size is continuous. Explain why he is wrong.
13.2

Bar charts, pictograms and line graphs

Year 7
S2
Video lesson: Bar charts, pictograms and line graphsComing soon
A pupil records the number of books read each day in a week. A bar chart shows the totals at a glance, and each bar must start at 0 so that the lengths can be compared fairly.

A pictogram uses a picture to stand for a number, and a key says what each picture means. A line graph joins points over time, so it shows change.

Mon12Tue9Wed15books

Key ideas

  • A bar chart: the bars start at 0 and have equal widths and gaps.
  • A pictogram: check the key to find the value of one picture; a half picture is half the key value.
  • A line graph shows change over time: read values across, then up or down.
  • Read the axis scale carefully: the marks may count in 2s, 5s or 10s.
Worked example 13.2.1
In a pictogram, one symbol stands for 5 pupils. A row has 6 symbols. How many pupils?

Method. Multiply the number of symbols by the key.

  1. Read the key. One symbol is 5 pupils.
    1 symbol = 5 pupils
  2. Multiply. 6 symbols are 6 × 5.
    30
  3. Write the answer. Give the answer with its unit.
    30 pupils

Check. 30 ÷ 5 = 6 symbols. ✓

Watch out. Use the key, not the number of symbols alone.

Worked example 13.2.2
The bar chart shows Monday 12, Tuesday 9 and Wednesday 15 books. Find the total.

Method. Add the three bars.

  1. Read the data. Write down the values before working out the statistic.
    12 + 9 + 15 = 36
  2. Add. Add the three values from the chart.
    12 + 9 + 15 = 36
  3. Write the answer. Give the answer with its unit.
    36 books

Check. 36 ÷ 3 = 12. ✓

Watch out. Add each bar once.

Worked example 13.2.3
A line graph shows the temperature at 9 am is 8°C and at 11 am is 14°C. Find the change.

Method. Subtract the earlier value from the later value.

  1. Read the data. Write down the values before working out the statistic.
    14 − 8 = 6
  2. Find the change. The temperature went up.
    14 − 8 = 6
  3. Write the answer. Give the answer with its unit.
    6°C rise

Check. 8 + 6 = 14. ✓

Watch out. Subtract the earlier from the later.

Watch out

Watch out: a bar chart does not have a value of "half a pupil". With a key of 5, a half symbol means 2.5 pupils; check the key before you count.

Exam tip

Grown-up tip. Ask the pupil to read the key first, and to say the value of one picture aloud before counting.

Exercise 13B  Bar charts, pictograms and line graphs

Non-calculator
1
FA pictogram has 1 symbol for 5 pupils. A row has 6 symbols. How many pupils?
2
FA pictogram has 1 symbol for 4 pupils. A row shows 3 and a half symbols. How many pupils?
3
FThe bar chart shows Monday 12, Tuesday 9 and Wednesday 15 books. Find the total.
4
FUsing the same chart, which day has the most books?
5
FUsing the same chart, how many more books on Wednesday than on Tuesday?
6
FA line graph shows the temperature at 9 am as 8°C and at 11 am as 14°C. Find the change.
7
FA table has 4 categories. How many bars does a bar chart of the table need?
8
PSA pictogram uses 1 symbol for 10 books. How many symbols are needed for 75 books?
9
PSSales rose from 40 in January to 65 in March. Find the increase.
10
FFor the bar chart values 5, 8 and 2: (a) the total (b) the largest value (c) the difference between the largest and the smallest
(a)(a) total of 5, 8 and 2
(b)(b) largest value
(c)(c) difference between 8 and 2
11
RSam says a bar chart should always start at 0. Explain why.
13.3

Mean, median, mode and range

Year 7
S1
Video lesson: Mean, median, mode and rangeComing soon
Five pupils score 3, 7, 2, 8 and 5 in a quiz. The mean is the total shared equally. The median is the middle value when the numbers are in order. The mode is the value that occurs most often. The range is the biggest value minus the smallest, and shows the spread.

For an even number of values, the median is the mean of the two middle values.

Key ideas

  • Mean = total of the values ÷ the number of values.
  • Median = the middle value after sorting (the mean of the two middle values when there are an even number).
  • Mode = the value that occurs most often (there can be more than one, or none).
  • Range = the biggest value − the smallest value.
Worked example 13.3.1
Find the mean, median and range of 3, 7, 2, 8 and 5.

Method. Work out each average and spread.

  1. Mean. Total 3 + 7 + 2 + 8 + 5 = 25, shared by 5.
    25 ÷ 5 = 5
  2. Median. In order: 2, 3, 5, 7, 8. The middle is 5.
    5
  3. Range. Biggest 8 − smallest 2.
    8 − 2 = 6
  4. Write the answer. Give the answer with its unit.
    mean 5, median 5, range 6

Check. Mean and median are both 5, range 6. ✓

Watch out. Sort before finding the median.

Worked example 13.3.2
Find the median of 2, 4, 6 and 8.

Method. There are four values, so the median is the mean of the two middle values.

  1. Find the middle two. In order: 2, 4, 6, 8; the middle two are 4 and 6.
    4 and 6
  2. Find the mean of these. Add and halve.
    (4 + 6) ÷ 2 = 5
  3. Write the answer. Give the answer with its unit.
    5

Check. The median lies between 4 and 6. ✓

Watch out. Halve the sum of the two middle values.

Worked example 13.3.3
Find the mode of 2, 3, 3, 5, 3 and 7.

Method. Count how many times each value occurs.

  1. Read the data. Write down the values before working out the statistic.
    3 appears 3 times
  2. Count the 3s. The value 3 occurs three times, more than any other.
    3 appears 3 times
  3. Write the answer. Give the answer with its unit.
    3

Check. Other values occur once. ✓

Watch out. The mode is the most common value.

Watch out

Watch out: the median needs the values in order first. Taking the median of 8, 3, 5 without sorting gives the wrong answer.

Exam tip

Grown-up tip. Ask the pupil to write the values on cards and move them into order before finding the median.

Exercise 13C  Mean, median, mode and range

Non-calculator
1
FFind the mean of 4, 6, 8 and 10.
2
FFind the median of 3, 9, 1, 7 and 5.
3
FFind the median of 2, 4, 6 and 8.
4
FFind the mode of 2, 3, 3, 5, 3 and 7.
5
FFind the range of 12, 5, 19 and 8.
6
FValues 1, 2 and 3 have frequencies 2, 2 and 1. Find the mean.
7
PSFive numbers have a mean of 8. Four of them are 6, 7, 9 and 10. Find the fifth number.
8
FFind the median and the range of 14, 9, 12 and 20.
9
FShoe sizes: 5, 6, 6, 7, 8, 8, 8. Find the mode and the median.
10
FFind: (a) the mean of 2, 4 and 9 (b) the median of 10, 2 and 7 (c) the range of 3, 15 and 9
(a)(a) mean of 2, 4 and 9
(b)(b) median of 10, 2 and 7
(c)(c) range of 3, 15 and 9
11
PSFive test scores average 60. Four are 55, 62, 68 and 70. Find the fifth score.
12
RExplain why the median can be better than the mean for the numbers 2, 3, 4 and 100.
13.4

Grouped data and the estimated mean

Year 7
S1, S2
Video lesson: Grouped data and the estimated meanComing soon
The heights of 20 pupils are grouped in ranges, because the exact heights are not needed. The mean can be estimated from the groups, using the middle value (the midpoint) of each group.

A grouped frequency table shows how many values lie in each group. The modal class is the group with the highest frequency. To estimate the mean: multiply each midpoint by its frequency, add the results, and divide by the total frequency.

Height (cm)Frequency
140 ≤ h < 1502
150 ≤ h < 1605
160 ≤ h < 1708
170 ≤ h < 1805

Key ideas

  • Midpoint of a group = (lower + upper) ÷ 2.
  • Estimated mean = (sum of midpoint × frequency) ÷ (total frequency).
  • The modal class is the group with the highest frequency.
  • Groups use ≤ and <: 150 ≤ h < 160 includes 150 but not 160.
Worked example 13.4.1
Using the table above, find the modal class.

Method. The group with the largest frequency.

  1. Compare the frequencies. The frequencies are 2, 5, 8 and 5.
    8 is the biggest
  2. Name the group. The frequency 8 belongs to 160 ≤ h < 170.
    160 ≤ h < 170
  3. Write the answer. Give the answer with its unit.
    160 ≤ h < 170

Check. 8 is the highest frequency. ✓

Watch out. The modal class has the highest frequency.

Worked example 13.4.2
Using the same table, estimate the mean height.

Method. Use the midpoints.

  1. Find the midpoints. 145, 155, 165 and 175.
    145, 155, 165, 175
  2. Multiply and add. 2 × 145 + 5 × 155 + 8 × 165 + 5 × 175 = 3260.
    3260
  3. Divide by the total frequency. The total frequency is 20.
    3260 ÷ 20 = 163
  4. Write the answer. Give the answer with its unit.
    163 cm

Check. The estimate is close to the middle group. ✓

Watch out. The estimate uses midpoints, not the exact heights.

Worked example 13.4.3
A grouped table has groups 0 to 10 with frequency 4 and 10 to 20 with frequency 4, and 20 to 30 with frequency 2. Find the midpoint of 20 to 30.

Method. Add the two ends and halve.

  1. Add. 20 + 30 = 50.
    50
  2. Halve. Midpoint = 50 ÷ 2.
    25
  3. Write the answer. Give the answer with its unit.
    25

Check. 25 is halfway between 20 and 30. ✓

Watch out. Use the midpoint, not the upper end.

Watch out

Watch out: the estimated mean is not always the exact mean. The midpoint assumes each value is in the middle of its group.

Exam tip

Grown-up tip. Ask the pupil to write the midpoint of each group in a column first, then multiply by the frequency in the next column.

Exercise 13D  Grouped data

Non-calculator
1
FUsing the height table (2, 5, 8, 5), find the modal class.
2
FUsing the height table, how many pupils are in the group 150 ≤ h < 160?
3
FUsing the height table, find the total frequency.
4
FFind the midpoint of the group 140 ≤ h < 150.
5
FUsing the height table, estimate the mean height.
6
PSUsing the height table, find the class that contains the median.
7
FBooks read by 12 pupils: groups 0 to 5 (4 pupils), 5 to 10 (6 pupils), 10 to 15 (2 pupils). Find the modal class.
8
PSUsing the books table (4, 6, 2 pupils in the groups 0 to 5, 5 to 10, 10 to 15), estimate the mean number of books. Use the midpoints 2.5, 7.5 and 12.5.
9
FFind the midpoint of: (a) the group 0 to 10 (b) the group 10 to 20 (c) the class width of 20 to 30
(a)(a) 0 to 10
(b)(b) 10 to 20
(c)(c) the class width of 20 to 30
10
PSThe class width of a grouped table is 5, and the first group is 10 to 15. Write the last group if there are 4 groups.
11
RExplain why the estimated mean may not equal the exact mean of the original heights.
13.5

Scatter graphs and correlation

Year 7
S3
Video lesson: Scatter graphs and correlationComing soon
Ten pupils record the hours spent revising and the marks they scored in a test. Plotting the points on a scatter graph shows whether more revision goes with higher marks. The pattern is called correlation.

Positive correlation: as one variable goes up, the other tends to go up. Negative correlation: as one goes up, the other tends to go down. No correlation: no clear pattern. A line of best fit is a straight line that follows the trend, and it can be used to estimate values.

Key ideas

  • Scatter graph: each point is one pair of values (x, y).
  • Positive correlation: points go up from left to right. Negative: points go down.
  • No correlation: the points are scattered with no pattern.
  • Correlation does not prove that one variable causes the other.
Worked example 13.5.1
A scatter graph of hours revised and marks has points going up from left to right. Describe the correlation.

Method. Look at the direction of the points.

  1. Read the data. Write down the values before working out the statistic.
    up from left to right
  2. Look. As the hours increase, the marks increase.
    up from left to right
  3. Write the answer. Give the answer with its unit.
    positive correlation

Check. More revision goes with higher marks. ✓

Watch out. Up from left to right is positive.

Worked example 13.5.2
Hot drinks sold go down as the temperature goes up. Describe the correlation.

Method. Look at the direction of the points.

  1. Read the data. Write down the values before working out the statistic.
    down from left to right
  2. Look. As the temperature rises, fewer hot drinks are sold.
    down from left to right
  3. Write the answer. Give the answer with its unit.
    negative correlation

Check. The points go down from left to right. ✓

Watch out. Down from left to right is negative.

Worked example 13.5.3
A line of best fit passes through (2, 40) and (8, 70). Estimate y when x = 6.

Method. Find the gradient, then use the line.

  1. Find the gradient. Gradient = (70 − 40) ÷ (8 − 2) = 30 ÷ 6.
    5
  2. Use the line. From (2, 40), go 4 across: 40 + 5 × 4.
    60
  3. Write the answer. Give the answer with its unit.
    60

Check. The line passes through (6, 60). ✓

Watch out. Use the gradient from the two points.

Watch out

Watch out: a correlation does not prove that one thing causes another. Ice cream sales and sunburn both rise in summer, but one does not cause the other.

Exam tip

Grown-up tip. Ask the pupil to draw a line of best fit by eye, with about as many points above as below it.

Exercise 13E  Scatter graphs and correlation

Non-calculator
1
FHours of revision and test marks: as the hours go up, the marks go up. What type of correlation is this?
2
FTemperature and number of hot drinks sold: as the temperature rises, fewer hot drinks are sold. What type of correlation is this?
3
FShoe size and maths score: there is no clear pattern. What type of correlation is this?
4
FA point (4, 9) on a scatter graph has x = hours and y = marks. How many marks for 4 hours?
5
FA line of best fit passes through (2, 40) and (8, 70). Find its gradient.
6
PSThe same line of best fit passes through (2, 40) and (8, 70). Estimate y when x = 6.
7
FThe points (1, 2), (2, 4), (3, 6) and (4, 20) are plotted. Which point is an outlier?
8
FA scatter graph of age and height for children aged 5 to 12 shows points going up. What correlation?
9
FDescribe the correlation: (a) points going down from left to right (b) points spread out with no pattern
(a)(a) points going down
(b)(b) points spread out
10
FPoints lie close to a straight line sloping up. Describe the correlation as weak or strong.
11
RSam says that because the marks go up with revision, revision must cause the higher marks. Is Sam right? Explain.
13.6

Comparing two sets of data

Year 7
S1
Video lesson: Comparing two sets of dataComing soon
Two teams score in a basketball league over five games. Both teams have the same mean, but one team is more consistent. To compare the two sets fairly, we use an average (the mean or median) and a measure of spread (the range).

When two sets have the same average, the set with the smaller range is more consistent: its values are closer together. When averages are different, compare them directly, and then compare the spread.

Key ideas

  • Compare an average (mean or median), and the spread (range).
  • A smaller range means the values are more consistent.
  • An outlier can change the mean a lot, but the median very little.
  • Give a reason with the comparison: "the range is smaller, so Team A is more consistent".
Worked example 13.6.1
Team A scores 10, 12 and 14. Team B scores 9, 12 and 15. Which team is more consistent?

Method. Compare the ranges, since the means are both 12.

  1. Find the ranges. Team A: 14 − 10 = 4. Team B: 15 − 9 = 6.
    4 and 6
  2. Compare. The smaller range is more consistent.
    Team A (4 < 6)
  3. Write the answer. Give the answer with its unit.
    Team A

Check. Both teams have mean 12, and 4 < 6. ✓

Watch out. Use the range to compare spread.

Worked example 13.6.2
Class X and class Y have a mean of 60. Class X has a range of 40, and class Y has a range of 10. Which class has more spread?

Method. Compare the ranges.

  1. Compare. The means are the same, so compare the spread.
    range 40 and 10
  2. Choose. The bigger range is class X.
    class X
  3. Write the answer. Give the answer with its unit.
    Class X

Check. Class X has the bigger range. ✓

Watch out. A bigger range means more spread.

Worked example 13.6.3
Find the median of 3, 9, 4, 6 and 8.

Method. Sort the values, then find the middle.

  1. Sort. 3, 4, 6, 8, 9.
    3, 4, 6, 8, 9
  2. Middle. The middle value is 6.
    6
  3. Write the answer. Give the answer with its unit.
    6

Check. Two values each side of 6. ✓

Watch out. Sort before finding the median.

Watch out

Watch out: two sets with the same mean are not always the same. Compare the spread (range) too, since it may be very different.

Exam tip

Grown-up tip. Ask the pupil to say "the mean is the same, but the range is different" before choosing which set is more consistent.

Exercise 13F  Comparing data sets

Non-calculator
1
FFind the mean of 2, 4, 6, 8 and 10.
2
FFind the range of 2, 4, 6, 8 and 10.
3
FTeam A scores 10, 12 and 14. Team B scores 9, 12 and 15. Which team is more consistent?
4
FShoe sizes of 5 pupils: 5, 6, 6, 7, 8. Find the median.
5
FTwo classes have a mean of 60. Class X has range 40 and class Y has range 10. Which class is more spread out?
6
FAli's five test marks are 60, 70, 80, 70 and 70. Find the mean.
7
PSSet P is 3, 5, 7 and set Q is 4, 5, 6. Which set has the smaller range?
8
RFor the shoe sizes of a class, which average is most useful: the mean, median or mode? Give a reason.
9
RSet P has mean 5 and median 4. Set Q has mean 5 and median 5. Which set has an outlier that pulls the mean up?
10
FFor the data 14, 9 and 22: (a) the range (b) the median (c) the mean
(a)(a) range
(b)(b) median
(c)(c) mean
11
PSFour pupils have a mean height of 150 cm. Three pupils are 148 cm, 152 cm and 155 cm. Find the height of the fourth pupil.
12
RSam says two sets with the same mean must be the same. Explain why this is not true.

Chapter summary

SkillMethod
Data typesCategorical; numerical discrete (counted); numerical continuous (measured)
ChartsBar charts start at 0; pictograms use a key; line graphs show change over time
AveragesMean = total ÷ count; median = middle when sorted; mode = most common
RangeBiggest minus smallest: a measure of spread
Grouped dataEstimated mean = sum of (midpoint × frequency) ÷ total frequency
Scatter graphsPositive, negative or no correlation; a line of best fit estimates values
Comparing dataCompare an average and the range; a smaller range is more consistent

Can you…?

  • I can tell categorical, discrete and continuous data apart
  • I can read and draw frequency tables, bar charts, pictograms and line graphs
  • I can find the mean, median, mode and range of a list and of a frequency table
  • I can estimate the mean of grouped data using midpoints
  • I can describe correlation and use a line of best fit to estimate a value
  • I can compare two sets of data using an average and the range

Key terms

categorical data
data in groups described by words, such as colours
discrete data
numerical data that is counted in whole steps
continuous data
numerical data that is measured and can take any value in a range
mean
the total of the values divided by the number of values
median
the middle value when the values are in order
mode
the value that occurs most often
range
the biggest value minus the smallest value
correlation
a link between two variables, shown by the pattern of points on a scatter graph
outlier
a value that is far away from the others

Exercise 13Z  Check-up

Non-calculator
1
Find the mean of 5, 7 and 9.
2
Find the median of 12, 4, 8 and 6.
3
Find the mode of 1, 2, 2, 3, 3 and 3.
4
Find the range of 9, 15 and 4.
5
A pictogram uses 1 symbol for 10 people. How many people are shown by 4 and a half symbols?
6
Groups 0 to 10 (2 pupils) and 10 to 20 (3 pupils): estimate the mean using midpoints 5 and 15.
7
The points of a scatter graph go down from left to right. What is the correlation?
8
Frequencies of a table are 3, 5 and 2. Find the total frequency.
9
Find the class that contains 23 in the groups 10 to 20, 20 to 25 and 25 to 30.
10
Four numbers have a mean of 6. Three are 4, 6 and 8. Find the fourth number.

Total 21 marks. Allow about 21 minutes.

Exercise 13X  Practice test questions

Non-calculator
1
FIs "number of goals scored" categorical, discrete or continuous?[1 mark]
2
FFind the median of 3, 8 and 5.[1 mark]
3
FFind the mean of 3, 5, 7 and 9.[2 marks]
4
FA pictogram uses 1 symbol for 8 books. A row shows 3 symbols. How many books?[2 marks]
5
FValues 2, 3 and 4 have frequencies 3, 5 and 2. Find the mean.[2 marks]
6
FFind the range and the mode of 4, 7, 7, 9 and 12.[2 marks]
7
FFive numbers have a mean of 10. Four of them are 8, 9, 12 and 11. Find the fifth number.[2 marks]
8
FHeights: groups 150 to 160 (4 pupils) and 160 to 170 (6 pupils). Estimate the mean height using the midpoints 155 and 165.[3 marks]
9
FA line of best fit passes through (0, 10) and (10, 30). Estimate y when x = 7.[3 marks]
10
RExplain why the median can be more useful than the mean for house prices.[3 marks]
← Chapter 12: Probability

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