Year 6 Pie Charts, Line Graphs and the Mean: check-up and SATs-style questions
Part of the Year 6 pie charts, line graphs and the mean chapter. Chapter overview · whole chapter on one page
Exercise 12Z Check-up
Non-calculatorKey words. A pie chart shows a whole split into sectors. Each sector is a slice of the circle. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Change the per cent into a fraction, then take that fraction of 360 degrees.
- Write the per cent as a fraction. Per cent means out of 100.25/100 = 1/4
- Take that fraction of the whole pie. The whole pie is 360 degrees.1/4 × 360 = 90
- Write the answer. The sector is this many degrees.90
Check. 25 per cent of 360 degrees is 90 degrees. ✓
Watch out. Use 360 degrees for the whole pie. Do not use 100 when you want degrees.
Key words. A pie chart shows a whole split into sectors. Each sector is a slice of the circle. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Turn the angle into a fraction of the whole pie, then find that fraction of the total.
- Write the sector as a fraction of the whole pie. The whole pie is 360 degrees, so divide the angle by 360.90 ÷ 360 = 1/4
- Take that fraction of the total. The total is 120, so take the same fraction of it.1/4 × 120 = 30
- Write the answer. Bananas has this many.30
Check. 30 out of 120 is the same fraction as 90 degrees out of 360. ✓
Watch out. Divide the angle by 360 first. Do not multiply the angle by the total.
Key words. A pie chart shows a whole split into sectors. Each sector is a slice of the circle. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Turn the angle into a fraction of the whole pie, then find that fraction of the total.
- Write the sector as a fraction of the whole pie. The whole pie is 360 degrees, so divide the angle by 360.48 ÷ 360 = 2/15
- Take that fraction of the total. The total is 30, so take the same fraction of it.2/15 × 30 = 4
- Write the answer. The sector has this many.4
Check. 4 out of 30 is the same fraction as 48 degrees out of 360. ✓
Watch out. Divide the angle by 360 first. Do not multiply the angle by the total.
Key words. A pie chart shows a whole split into sectors. Each sector is a slice of the circle. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Find the fraction of the whole, then multiply by 100 to get per cent.
- Write the sector as a fraction of the total. Football is 12 out of 40.12 ÷ 40 = 3/10
- Change the fraction to per cent. Per cent means out of 100, so multiply by 100.3/10 × 100 = 30
- Write the answer. This is the per cent of the whole.30
Check. 30 per cent of 40 is 12, because 30 out of 100 is the same as 3/10. ✓
Watch out. Per cent is out of 100. A fraction with a bottom number of 100 is easy to read.
Key words. A line graph marks a point for each time or week, and joins the points with straight lines. The scale is the numbers up the side. The lines across the graph are the gridlines.
Method. Find the label, go up to the point, then go across to the scale.
- Find the time or week along the bottom. Find Jun on the horizontal line.Jun
- Go up to the line. Go straight up from the label to the point. Do not read the line between two points.the point for Jun
- Go across to the scale. Read the number on the scale level with the point. The scale is in mm.Rainfall in June = 70
Check. The point sits on a gridline, so the reading is exact. ✓
Watch out. Read the point itself. A line between two points only shows the change.
Key words. A line graph marks a point for each time or week, and joins the points with straight lines. The scale is the numbers up the side. The lines across the graph are the gridlines.
Method. Find the point at that height, then go down to the label along the bottom.
- Find the value on the scale. Find the level of 40 on the scale.40
- Go along the line to that point. Find the point at this level, then go down to the bottom of the graph.the point at 40
- Read the label along the bottom. This is the time or week for the rainfall of 40 mm.Feb
Check. Only Feb reaches 40. ✓
Watch out. Start from the value on the scale, not from the bottom. Check the other points too.
Key words. A line graph marks a point for each time or week, and joins the points with straight lines. The scale is the numbers up the side. The lines across the graph are the gridlines.
Method. Find the label, go up to the point, then go across to the scale.
- Find the time or week along the bottom. Find Round 3 on the horizontal line.Round 3
- Go up to the line. Go straight up from the label to the point. Do not read the line between two points.the point for Round 3
- Go across to the scale. Read the number on the scale level with the point. The scale is in points.the Blue team in round 3 = 45
Check. The point sits on a gridline, so the reading is exact. ✓
Watch out. Read the point itself. A line between two points only shows the change.
Key words. The mean is the same as the average. Add all the values to get the total, then share the total equally between the number of values.
Method. Add all the values, then share the total equally between the number of values.
- Write the values. These are all the values. Count every one, even a zero.8, 10, 12, 14, 6
- Add the values to find the total. The total is what all the values make together.8 + 10 + 12 + 14 + 6 = 50
- Count the values. Count how many numbers there are. Do not count the total.There are 5 values
- Divide the total by the number of values. Sharing the total equally between the values gives the mean.50 ÷ 5 = 10
Check. 10 × 5 = 50, so the mean is right. ✓
Watch out. Divide by how many values there are, not by the biggest value. Do not forget to count a zero.
Key words. The mean is the same as the average. Add all the values to get the total, then share the total equally between the number of values.
Method. Find the total from the mean, then take away the values you know.
- Work out 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 in the list.6 + 9 + 11 = 26
- Take the known total away from the total. The missing value is what is left over.32 − 26 = 6
- Write the answer. This is the missing value.6
Check. 26 + 6 = 32, and 32 ÷ 4 = 8. ✓
Watch out. Find the total first. Do not take away the mean from one value.
Key words. The mean is the same as the average. Add all the values to get the total, then share the total equally between the number of values.
Method. Add all the values, then share the total equally between the number of values.
- Write the values. These are all the values. Count every one, even a zero.3, 6, 9
- Add the values to find the total. The total is what all the values make together.3 + 6 + 9 = 18
- Count the values. Count how many numbers there are. Do not count the total.There are 3 values
- Divide the total by the number of values. Sharing the total equally between the values gives the mean.18 ÷ 3 = 6
Check. 6 × 3 = 18, so the mean is right. ✓
Watch out. Divide by how many values there are, not by the biggest value. Do not forget to count a zero.
Key words. The mean is the same as the average. Add all the values to get the total, then share the total equally between the number of values.
Method. Add all the values, then share the total equally between the number of values.
- Write the values. These are all the values. Count every one, even a zero.2, 8, 5
- Add the values to find the total. The total is what all the values make together.2 + 8 + 5 = 15
- Count the values. Count how many numbers there are. Do not count the total.There are 3 values
- Divide the total by the number of values. Sharing the total equally between the values gives the mean.15 ÷ 3 = 5
Check. 5 × 3 = 15, so the mean is right. ✓
Watch out. Divide by how many values there are, not by the biggest value. Do not forget to count a zero.
Total 21 marks. Allow about 21 minutes.
Exercise 12X SATs-style questions
Non-calculatorKey words. A pie chart shows a whole split into sectors. Each sector is a slice of the circle. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Change the per cent into a fraction, then take that fraction of the total.
- Write the per cent as a fraction. Per cent means out of 100.40/100 = 2/5
- Take that fraction of the total. The total is 75, so take 2/5 of it.2/5 × 75 = 30
- Write the answer. Walk has this many.30
Check. 30 is 2/5 of 75, so 40 per cent of 75 is 30. ✓
Watch out. Per cent is out of 100, not out of the total. Change it to a fraction first.
Key words. A line graph marks a point for each time or week, and joins the points with straight lines. The scale is the numbers up the side. The lines across the graph are the gridlines.
Method. Find the label, go up to the point, then go across to the scale.
- Find the time or week along the bottom. Find Round 4 on the horizontal line.Round 4
- Go up to the line. Go straight up from the label to the point. Do not read the line between two points.the point for Round 4
- Go across to the scale. Read the number on the scale level with the point. The scale is in points.the Blue team in round 4 = 40
Check. The point sits on a gridline, so the reading is exact. ✓
Watch out. Read the point itself. A line between two points only shows the change.
Key words. The mean is the same as the average. Add all the values to get the total, then share the total equally between the number of values.
Method. Add all the values, then share the total equally between the number of values.
- Write the values. These are all the values. Count every one, even a zero.6, 8, 10, 12
- Add the values to find the total. The total is what all the values make together.6 + 8 + 10 + 12 = 36
- Count the values. Count how many numbers there are. Do not count the total.There are 4 values
- Divide the total by the number of values. Sharing the total equally between the values gives the mean.36 ÷ 4 = 9
Check. 9 × 4 = 36, so the mean is right. ✓
Watch out. Divide by how many values there are, not by the biggest value. Do not forget to count a zero.
Key words. A pie chart shows a whole split into sectors. Each sector is a slice of the circle. 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 whole pie. A whole pie chart is a whole circle, and a whole circle is 360 degrees.whole pie = 360°
- Write the sector as a fraction of the total. Car is 10 out of 60, so divide 10 by 60.10 ÷ 60 = 1/6
- Multiply the fraction by 360 degrees. The fraction tells us the share of the whole circle.1/6 × 360 = 60
- Write the answer. The sector is this many degrees.60
Check. All the sector angles in a pie chart add up to 360 degrees. ✓
Watch out. Use 360 degrees for the whole pie, not 100. The 100 is only for percentages.
Key words. A pie chart shows a whole split into sectors. Each sector is a slice of the circle. The whole pie is 360 degrees, and it is also 100 per cent.
Method. Change the per cent into a fraction, then take that fraction of the total.
- Write the per cent as a fraction. Per cent means out of 100.35/100 = 7/20
- Take that fraction of the total. The total is 40, so take 7/20 of it.7/20 × 40 = 14
- Write the answer. Dogs has this many.14
Check. 14 is 7/20 of 40, so 35 per cent of 40 is 14. ✓
Watch out. Per cent is out of 100, not out of the total. Change it to a fraction first.
Key words. The change is how much a value has gone up or down. To find it, take the first value away from the second value.
Method. Take the start value away from the end value.
- Read the value at the start. The first point is 09:00.09:00 = 25
- Read the value at the end. The second point is 11:00.11:00 = 40
- Find the rise. Take the start value away from the end value.40 − 25 = 15
- Write the answer. 15
Check. 25 + 15 = 40. ✓
Watch out. Start with the earlier point. A rise is positive, and a fall would be the other way round.
Key words. The mean is the same as the average. Add all the values to get the total, then share the total equally between the number of values.
Method. Find the total from the mean, then take away the values you know.
- Work out the total from the mean. The total is the mean times the number of values.7 × 5 = 35
- Add the values you know. These values are already in the list.3 + 9 + 5 + 8 = 25
- Take the known total away from the total. The missing value is what is left over.35 − 25 = 10
- Write the answer. This is the missing value.10
Check. 25 + 10 = 35, and 35 ÷ 5 = 7. ✓
Watch out. Find the total first. Do not take away the mean from one value.
Key words. A line graph marks a point for each time or week, and joins the points with straight lines. The scale is the numbers up the side. The lines across the graph are the gridlines.
Method. Read every value you need, then add them all together.
- Read each value you need. Find each point on the graph, one at a time.Week 1 30, Week 2 50, Week 3 40, Week 4 70, Week 5 60
- Add the values. Add them all together to find the total.30 + 50 + 40 + 70 + 60 = 250
- Write the answer. This is the total for all five weeks.250
Check. Add them in a different order to check: the total is still 250. ✓
Watch out. Make sure you have read every point, including the last one.
Key words. The mean is the same as the average. Add all the values to get the total, then share the total equally between the number of values.
Method. Add all the values, then share the total equally between the number of values.
- Write the values. These are all the values. Count every one, even a zero.30, 50, 40, 70, 60
- Add the values to find the total. The total is what all the values make together.30 + 50 + 40 + 70 + 60 = 250
- Count the values. Count how many numbers there are. Do not count the total.There are 5 values
- Divide the total by the number of values. Sharing the total equally between the values gives the mean.250 ÷ 5 = 50
Check. 50 × 5 = 250, so the mean is right. ✓
Watch out. Divide by how many values there are, not by the biggest value. Do not forget to count a zero.
Key words. The mean is the same as the average. Add all the values to get the total, then share the total equally between the number of values.
Method. Compare each value with the mean, and list only the values that are higher.
- Compare each value with the mean. The mean is 50.Week 1 30; Week 2 50; Week 3 40; Week 4 70; Week 5 60
- List the values above 50. A value equal to 50 is not above the mean.Week 4, Week 5
- Write the answer. Week 4 and Week 5
Check. A value equal to 50 is not above the mean, so it is left out of the list. ✓
Watch out. Be careful with a value equal to the mean. It is not above the mean.
Key words. The change is how much a value has gone up or down. To find it, take the first value away from the second value.
Method. Read both values, then take the smaller one away from the bigger one.
- Read the first value. The Red team is 60 points.the Red team = 60
- Read the second value. The Blue team is 55 points.the Blue team = 55
- Find the difference. The Red team is the bigger, so take the smaller value away.60 − 55 = 5
- Write the answer. 5
Check. 55 + 5 = 60, so the difference is right. ✓
Watch out. Subtract the smaller value from the bigger value. The answer is never negative.
Key words. A line graph marks a point for each time or week, and joins the points with straight lines. The scale is the numbers up the side. The lines across the graph are the gridlines.
Method. Count only the rounds where the Red team has more points.
- Compare the two teams in each round. Read both values for every round.Round 1: 20 and 40; Round 2: 30 and 30; Round 3: 35 and 45; Round 4: 50 and 40; Round 5: 60 and 55
- Count the rounds where the Red team scored more. Only count the rounds where the Red team is higher.Round 4, Round 5
- Write the answer. 2
Check. Every round was checked, and the rounds where the other team scored more are not counted. ✓
Watch out. Count the rounds, not the points. Check each round one at a time.
Key words. The mean is the same as the average. Add all the values to get the total, then share the total equally between the number of values.
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 average of the values.mean 12, number of values 5
- Multiply the mean by the number of values. Sharing the total equally gave the mean, so multiplying gives the total back.12 × 5 = 60
- Write the answer. This is the total of all the values.60
Check. 60 ÷ 5 = 12, so the mean is right. ✓
Watch out. Multiply to find the total from a mean. Divide only when you need the mean from a total.
Key words. The mean is the same as the average. Add all the values to get the total, then share the total equally between the number of values.
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 average of the values.mean 15, number of values 5
- Multiply the mean by the number of values. Sharing the total equally gave the mean, so multiplying gives the total back.15 × 5 = 75
- Write the answer. This is the total of all the values.75
Check. 75 ÷ 5 = 15, so the mean is right. ✓
Watch out. Multiply to find the total from a mean. Divide only when you need the mean from a total.
Key words. The mean is the same as the average. Add all the values to get the total, then share the total equally between the number of values.
Method. Turn each mean back 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 its number of values.12 × 5 = 60
- Find the total of the second group. Multiply its mean by its number of values.15 × 5 = 75
- Add the two totals. Together the two groups have this total.60 + 75 = 135
- Count everybody and divide. There are 5 + 5 = 10 values altogether.135 ÷ 10 = 13.5
Check. 13.5 × 10 = 135, so the combined mean is right. ✓
Watch out. Do not just average the two means. That only works when both groups have the same number of values.
Key words. The mean is the same as the average. Add all the values to get the total, then share the total equally between the number of values.
Method. Check whether the two groups have the same number of values.
- Check the sizes of the groups. Both classes have 5 children, so the groups are the same size.5 and 5
- Test the rule with groups of different sizes. Take 2 children with a mean of 10, and 8 children with a mean of 20. Find the mean of all 10 children.(2 × 10 + 8 × 20) ÷ 10 = (20 + 160) ÷ 10 = 18, but (10 + 20) ÷ 2 = 15
- Decide. Averaging the two means only works when the groups have the same number of values.Only when the groups are the same size
Check. With equal groups, (12 + 15) ÷ 2 = 13.5, which matches the combined mean. ✓
Watch out. In general, add the two totals and divide by the number of children altogether.