Year 6 Maths reasoning (SATs) Statistics and data: check-up and practice test questions

Method. Read the values from the table, then add them.

1. Find the values you need. Read the values for Bus and Cycle from the table.
   18 + 9
2. Add them together. Add the values.
   18 + 9 = 27
3. Write the answer.
   27

Check. 27 is the sum of the chosen values. ✓

Method. Subtract the smaller value from the larger value.

1. Read the two values. Walk has 25 and Bus has 18.
   25 and 18
2. Subtract the smaller from the bigger. Find how many more Walk there are than Bus.
   25 - 18 = 7
3. Write the answer.
   7

Check. 18 + 7 = 25. ✓

Method. Find the fraction of the total, then multiply by 360.

1. Share of the total. Dance is 24 out of 60.
   24 / 60
2. Work out the angle. A whole pie is 360 degrees, so multiply the share by 360.
   24 / 60 x 360 = 144
3. Write the answer.
   144

Check. 144 / 360 = 24 / 60. ✓

Watch out. Make sure all the sector angles add up to 360.

Method. Find the fraction of the whole pie, then multiply by the total.

1. Share of the pie. The sector is 90 of the 360 degrees.
   90 / 360
2. Multiply by the total. Multiply the share by the total of 36.
   90 / 360 x 36 = 9
3. Write the answer.
   9

Check. 9 / 36 = 90 / 360. ✓

Method. Subtract the earlier reading from the later one.

1. Read the two values. At 6 am it is 5 degrees C, and at 2 pm it is 15 degrees C.
   5 and 15
2. Find the change. Subtract the first reading from the second.
   15 - 5 = 10
3. Write the answer.
   10 degrees C

Check. 5 + 10 = 15. ✓

Method. The mean is the total divided by the number of values.

1. Add the values. Add up all 4 values.
   6 + 8 + 10 + 12 = 36
2. Share equally. Divide the total by the number of values, 4.
   36 / 4 = 9
3. Write the answer.
   9 cm

Check. 9 x 4 = 36. ✓

Watch out. Check that the total of the values is the mean times the number of values.

Method. Multiply the mean by the number of values, then take away the known values.

1. Total needed. The mean is 8 for 4 values, so the total is 8 x 4.
   8 x 4 = 32
2. Subtract the known values. Take away the values you already know.
   32 - 20 = 12
3. Write the answer.
   12

Check. 20 + 12 = 32. ✓

Watch out. Find the total first, then the missing value.

Method. Order the values, then find the middle one.

1. Put the values in order. Write them from smallest to largest.
   2, 4, 8, 11, 15
2. Find the middle. With 5 values, the middle value is 8.
   8
3. Write the answer.
   8

Check. There are 2 values on each side of 8. ✓

Watch out. Always order the values first. The median is not the first or the last value.

Method. Count how often each value appears, and choose the most common.

1. Count how many times each value appears. 3 appears 3 time(s), 7 appears 2 time(s), 9 appears 1 time(s)
   3 appears 3 times
2. Choose the most common. The mode is the value that appears most often.
   3
3. Write the answer.
   3

Check. 3 appears 3 times, which is the most. ✓

Method. Range = largest value minus smallest value.

1. Find the largest and smallest values. The largest is 22 and the smallest is 6.
   22 and 6
2. Subtract. The range is the largest minus the smallest.
   22 - 6 = 16
3. Write the answer.
   16

Check. 6 + 16 = 22. ✓

Method. Read the values from the table, then add them.

1. Find the values you need. Read the values for Walk and Car from the table.
   25 + 12
2. Add them together. Add the values.
   25 + 12 = 37
3. Write the answer.
   37

Check. 37 is the sum of the chosen values. ✓

Method. Subtract the smaller value from the larger value.

1. Read the two values. Apples has 120 and Plums has 60.
   120 and 60
2. Subtract the smaller from the bigger. Find how many more Apples there are than Plums.
   120 - 60 = 60
3. Write the answer.
   60

Check. 60 + 60 = 120. ✓

Method. Find the fraction of the total, then multiply by 360.

1. Share of the total. Reading is 30 out of 90.
   30 / 90
2. Work out the angle. A whole pie is 360 degrees, so multiply the share by 360.
   30 / 90 x 360 = 120
3. Write the answer.
   120

Check. 120 / 360 = 30 / 90. ✓

Watch out. Make sure all the sector angles add up to 360.

Method. Find the fraction of the whole pie, then multiply by the total.

1. Share of the pie. The sector is 80 of the 360 degrees.
   80 / 360
2. Multiply by the total. Multiply the share by the total of 36.
   80 / 360 x 36 = 8
3. Write the answer.
   8

Check. 8 / 36 = 80 / 360. ✓

Method. Multiply the mean by the number of values, then take away the known values.

1. Total needed. The mean is 7 for 4 values, so the total is 7 x 4.
   7 x 4 = 28
2. Subtract the known values. Take away the values you already know.
   28 - 20 = 8
3. Write the answer.
   8

Check. 20 + 8 = 28. ✓

Watch out. Find the total first, then the missing value.

Method. Order the values, then find the middle one.

1. Put the values in order. Write them from smallest to largest.
   3, 5, 9, 12, 20
2. Find the middle. With 5 values, the middle value is 9.
   9
3. Write the answer.
   9

Check. There are 2 values on each side of 9. ✓

Watch out. Always order the values first. The median is not the first or the last value.

Method. Range = largest value minus smallest value.

1. Find the largest and smallest values. The largest is 15 and the smallest is 3.
   15 and 3
2. Subtract. The range is the largest minus the smallest.
   15 - 3 = 12
3. Write the answer.
   12

Check. 3 + 12 = 15. ✓

Method. Subtract the earlier reading from the later one.

1. Read the two values. At Jan it is 20 cm, and at Jul it is 29 cm.
   20 and 29
2. Find the change. Subtract the first reading from the second.
   29 - 20 = 9
3. Write the answer.
   9 cm

Check. 20 + 9 = 29. ✓

Method. Compare the two ranges.

1. Compare the ranges. P has a range of 2 and Q has a range of 12.
   2 < 12
2. Decide. P is more consistent.
   Team P
3. Write the answer.
   Team P, because its range of 2 is smaller, so its scores are closer together.

Check. 2 < 12. ✓

Method. The mean does not show how the scores are spread.

1. What the mean shows. The mean is the average of all the scores.
   average
2. Conclude. Some scores may be above 9 and some below, so most may not be 9.
   no
3. Write the answer.
   no

Check. A mean of 9 can come from very different scores. ✓