Year 6 Maths reasoning (SATs) · Statistics and data · Lesson 8.5

Year 6 Maths reasoning (SATs): Comparing data sets and valid conclusions

Part of the Year 6 Maths reasoning (SATs) statistics and data chapter. Chapter overview · whole chapter on one page

8.5

Comparing data sets and valid conclusions

Year 6
Compare two data sets and explain which is more suitable, and why (Year 6), Say whether a conclusion from a graph is valid, and explain (Year 6)

Story. Two football teams have scored the same total number of goals in five matches. Coach Ruth wants to know which team is more consistent, because her team plays best when it scores about the same every match.

Rule

Two data sets can have the same mean but very different spreads. The range shows how spread out the values are.

A conclusion is valid only if the data support it. A link in a graph does not prove that one thing causes another.

Key ideas

Same mean does not mean same spread: compare the range too.
A smaller range means more consistent results.
Check whether a conclusion goes beyond what the data show.

Worked example 8.5.1

Team A scored 5, 6, 7, 6, 6 goals. Team B scored 1, 6, 6, 6, 11 goals. Which team is more consistent? Write A or B.

Method. Compare the ranges, because a smaller range means more consistent scores.

Range A. Largest 7, smallest 5, so the range is 2.
7 - 5 = 2
Range B. Largest 11, smallest 1, so the range is 10.
11 - 1 = 10
Compare. Team A has the smaller range, so its scores are more consistent.
A
Write the answer.
A

Check. 2 < 10, and both teams have a mean of 6. ✓

Worked example 8.5.2

Ben says that because ice cream sales go up on hot days, ice cream makes the weather hotter. Is his conclusion valid? Write yes or no.

Method. A link between two things does not show that one causes the other.

What the data show. Sales and hot days go up together.
a link
Is it a cause? Ice cream cannot make the weather hotter, so the conclusion does not follow.
no
Write the answer.
no

Check. A link is not proof of cause. ✓

Worked example 8.5.3

Two classes have a mean score of 12. Class A has a range of 3 and Class B has a range of 15. Which class has more consistent scores? Write A or B.

Method. Compare the ranges: the smaller range means more consistent scores.

Range of A. The range of Class A is 3.
3
Range of B. The range of Class B is 15.
15
Compare. A has the smaller range, so its scores are more consistent.
A
Write the answer.
A

Check. 3 < 15. ✓

Watch out

Watch out. Two data sets with the same mean can be very different. Always check the range or the spread.

Exam tip

Practice guide. Write one sentence that compares the averages and one that compares the spread.

Exercise 8E Practice: comparing data sets and conclusions

Non-calculator

RTeam X scored 4, 5, 6, 5, 5 goals. Team Y scored 2, 5, 5, 5, 8 goals. Which team is more consistent? Write X or Y.

Done

RAli and Sam both have a mean score of 12 in a quiz. Ali has a range of 3, and Sam has a range of 15. Who had more consistent scores? Write Ali or Sam.

Done

RTwo shops sell the same shoes. One shop says its average shoe size is 6, so most people buy size 6. Explain why this might not be true.

Done

RA graph shows that the number of umbrellas sold goes up when it rains. Which conclusion is valid? Choose one: Umbrellas sold go up when it rains, Rain is caused by umbrella sales or Umbrella sellers make it rain.

Done

RA bar chart shows the average for two classes. Class 1 has a mean of 20 and Class 2 has a mean of 24. Is Class 2 better at the test? Write yes or no.

Done

PSFour journeys to school. The values are 12, 14, 16, 18 minutes. What is the mean, in minutes?

Done

PSFind the median of these values: 2, 9, 4, 12, 7.

Done

RExplain why the mode can be a useful average for shoe sizes.

Done