Year 6: Statistics: pie charts, line graphs and the mean
Part of the Year 6 sats maths revision chapter. Chapter overview · whole chapter on one page
Statistics: pie charts, line graphs and the mean
A pie chart shows a whole split into sectors. The whole pie is 360 degrees, or 100 per cent. To find the angle of a sector, take its fraction of the total and multiply by 360. To find the number in a sector from its angle, divide the angle by 360 and multiply by the total.
A line graph joins points with straight lines. Read a point by going up from its label to the line, then across to the scale. The change between two points is the later value minus the earlier value.
The mean is the average. Add all the values, then divide by the number of values. Count every value, including a zero. If you know the mean and the number of values, multiply to find the total.
Key ideas
- Pie chart: angle = fraction of the total × 360 degrees.
- Line graph: read the point, go across to the scale. Change = end value minus start value.
- Mean = total ÷ number of values. Total = mean × number of values.
- The angles of a pie chart add up to 360 degrees.
Key words. A pie chart shows a whole split into sectors. A sector is one slice of the pie. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Find the fraction of the whole pie, then take that fraction of 360 degrees.
- Write the sector and the total. The sector is one part of the whole pie.Bus: 30 out of 120
- Write the sector as a fraction of the total. Bus is 30 out of 120.30 ÷ 120 = 1/4
- Multiply by 360 degrees. The whole pie is 360 degrees.1/4 × 360 = 90
Check. All the sectors must add up to 360 degrees. ✓
Watch out. Use 360 degrees for the whole pie, not 100.
Key words. A line graph marks a point for each time, and joins the points with straight lines. The scale shows the value of each point. The change is the end value minus the start value.
Method. Subtract the start value from the end value.
- Read the value at Tue. This is the start value.Tue = 30
- Read the value at Fri. This is the end value.Fri = 60
- Take the start value from the end value. The change is the end value minus the start value.60 − 30 = 30
Check. 30 + 30 = 60. ✓
Watch out. Start with the earlier point. Subtract the smaller value from the bigger value.
Key words. The mean is the average: add all the values, then share the total equally between the number of values. The total is all the values added together.
Method. Add the values, then divide the total by the number of values.
- Add all the values. Count every value, including a zero.4 + 7 + 9 + 10 = 30
- Count the values. Count how many numbers there are.there are 4 values
- Divide the total by the number of values. Sharing the total equally gives the mean.30 ÷ 4 = 7.5
Check. 7.5 × 4 = 30, so the mean is right. ✓
Watch out. Divide by the number of values, not by the biggest value.
Watch out
Common mistake: dividing the total by the biggest value instead of by the number of values, or forgetting to count a zero. Also, for a pie chart use 360 degrees, not 100, when you want an angle.
Exercise 13G Timed set: pie charts, line graphs and the mean (about 12 minutes)
Non-calculatorKey words. A pie chart shows a whole split into sectors. A sector is one slice of the pie. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Divide the angle by 360, then take that fraction of the total.
- Write the angle as a fraction of 360. The whole pie is 360 degrees.72 ÷ 360 = 1/5
- Take that fraction of the total. The total is 150.1/5 × 150 = 30
Check. 30 out of 150 is the same fraction as 72 degrees out of 360. ✓
Watch out. Divide the angle by 360 first, not the total.
Key words. A pie chart shows a whole split into sectors. A sector is one slice of the pie. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Find the fraction of the whole pie, then take that fraction of 360 degrees.
- Write the sector and the total. The sector is one part of the whole pie.Pasta: 18 out of 60
- Write the sector as a fraction of the total. Pasta is 18 out of 60.18 ÷ 60 = 3/10
- Multiply by 360 degrees. The whole pie is 360 degrees.3/10 × 360 = 108
Check. All the sectors must add up to 360 degrees. ✓
Watch out. Use 360 degrees for the whole pie, not 100.
Key words. A pie chart shows a whole split into sectors. A sector is one slice of the pie. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Write the sector as a fraction of the total, then multiply by 100.
- Write the sector as a fraction of the total. Walk is 15 out of 60.15 ÷ 60 = 1/4
- Change it to per cent. Per cent means out of 100.1/4 × 100 = 25
Check. 25 per cent of 60 is 15. ✓
Watch out. Per cent is out of 100.
Key words. A pie chart shows a whole split into sectors. A sector is one slice of the pie. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Change each per cent into an angle, then add the angles together.
- Change each per cent to an angle. Each angle is the per cent of 360 degrees.35 per cent: 35 ÷ 100 × 360 = 126°; 25 per cent: 25 ÷ 100 × 360 = 90°; 20 per cent: 20 ÷ 100 × 360 = 72°; 20 per cent: 20 ÷ 100 × 360 = 72°
- Add the angles. The angles of a pie chart must add up to 360 degrees.126 + 90 + 72 + 72 = 360
Check. 360 degrees is a whole turn, so the sectors fill the pie exactly. ✓
Watch out. Add the angles, not the per cents, when you check the whole pie.
Key words. A line graph marks a point for each time, and joins the points with straight lines. The scale shows the value of each point. The change is the end value minus the start value.
Method. Find the label, go up to the point, then read across to the scale.
- Find Wed along the bottom. Start at the label.Wed
- Go straight up to the point. Go up from the label to the point, and do not read the line between points.the point for Wed
- Read across to the scale. Read the number on the scale level with the point.the sales on Wednesday = 50
Check. The point sits on a gridline, so the reading is exact. ✓
Watch out. Read the point, not the line between two points.
Key words. A line graph marks a point for each time, and joins the points with straight lines. The scale shows the value of each point. The change is the end value minus the start value.
Method. Subtract the start value from the end value.
- Read the value at Mon. This is the start value.Mon = 20
- Read the value at Fri. This is the end value.Fri = 60
- Take the start value from the end value. The change is the end value minus the start value.60 − 20 = 40
Check. 20 + 40 = 60. ✓
Watch out. Start with the earlier point. Subtract the smaller value from the bigger value.
Key words. The mean is the average: add all the values, then share the total equally between the number of values. The total is all the values added together.
Method. Add the values, then divide the total by the number of values.
- Add all the values. Count every value, including a zero.8 + 10 + 12 + 14 + 6 = 50
- Count the values. Count how many numbers there are.there are 5 values
- Divide the total by the number of values. Sharing the total equally gives the mean.50 ÷ 5 = 10
Check. 10 × 5 = 50, so the mean is right. ✓
Watch out. Divide by the number of values, not by the biggest value.
Key words. The mean is the average: add all the values, then share the total equally between the number of values. The total is all the values added together.
Method. Add the values, then divide the total by the number of values.
- Add all the values. Count every value, including a zero.2 + 5 + 0 + 3 = 10
- Count the values. Count how many numbers there are.there are 4 values
- Divide the total by the number of values. Sharing the total equally gives the mean.10 ÷ 4 = 2.5
Check. 2.5 × 4 = 10, so the mean is right. ✓
Watch out. Divide by the number of values, not by the biggest value.
Key words. The mean is the average: add all the values, then share the total equally between the number of values. The total is all the values added together.
Method. Find the total from the mean, then take away the values you know.
- Find the total from the mean. The total is the mean times the number of values.8 × 4 = 32
- Add the values you know. These values are already given.6 + 9 + 11 = 26
- Take the known total from the total. The missing value is what is left over.32 − 26 = 6
Check. 26 + 6 = 32, and 32 ÷ 4 = 8. ✓
Watch out. Find the total first. Do not subtract the mean from one value.
Key words. The mean is the average: add all the values, then share the total equally between the number of values. The total is all the values added together.
Method. Multiply the mean by the number of values to get the total.
- Write the mean and the number of values. The mean is the total shared equally.mean 12, number of values 6
- Multiply the mean by the number of values. Multiplying gives the total back.12 × 6 = 72
Check. 72 ÷ 6 = 12, so the total is right. ✓
Watch out. Multiply to find the total from the mean.
Key words. The mean is the average: add all the values, then share the total equally between the number of values. The total is all the values added together.
Method. Turn each mean into a total, add the totals, then divide by the number of values altogether.
- Find the total of the first group. Multiply its mean by the number of values.12 × 5 = 60
- Find the total of the second group. Do the same for the second group.15 × 5 = 75
- Add the totals and count everyone. There are 5 + 5 = 10 values altogether.60 + 75 = 135, and 135 ÷ 10 = 13.5
Check. 13.5 × 10 = 135, so the combined mean is right. ✓
Watch out. Do not average the two means unless both groups have the same number of values.
Key words. The mean is the average: add all the values, then share the total equally between the number of values. The total is all the values added together.
Method. Work out the mean of a set of numbers, then check whether it is one of them.
- Work out the mean. Add the values, then divide by how many there are.(1 + 2 + 6) ÷ 3 = 3
- Compare the mean with the values. Look to see if the mean is one of the numbers in the list.3 is not one of 1, 2, 6
- Write the answer. One example is enough to show that the mean is not always a value in the list.No
Check. Another set, such as 2, 4 and 6, has the mean 4, which is one of the values. So the answer depends on the numbers. ✓
Watch out. One example that does not match is enough to show that a statement is not always true.