Sec 4 E-Math · Statistics

Comparing two data sets questions with answers

Practice questions on comparing two data sets, from the basics up to exam level, each with a full worked solution. Try them on paper first, then open the solution to check your working.

Worked example

In a test, class $A$ had a mean of $71$ marks and a standard deviation of $11.5$ marks. Class $B$ had a mean of $68$ marks and a standard deviation of $10.2$ marks. Which class's results were more consistent?

Step 1 of 3

Which measure answers the question?

More consistent means less spread: the smaller standard deviation.

Try a question: Comparing two data sets

Free · no sign-up

Answer a real practice question. Get it wrong and MugCorner shows you where it went wrong, with hints and a step-by-step guide.

Questions

Question 1Compare by mean and sd
In a test, class $A$ had a mean of $62$ marks and a standard deviation of $6.3$ marks. Class $B$ had a mean of $65$ marks and a standard deviation of $7.9$ marks. Which class did better on average?
Show the worked solution
1. Step 1: Which measure answers the question?Better on average means the higher mean.
2. Step 2: Compare the two classes' values of that measureClass A's is lower.
3. Step 3: So the answer isClass B.
Question 2Compare by mean and sd
In a test, class $A$ had a mean of $62$ marks and a standard deviation of $8.4$ marks. Class $B$ had a mean of $65$ marks and a standard deviation of $12.1$ marks. Which class's results were more consistent?
Show the worked solution
1. Step 1: Which measure answers the question?More consistent means less spread: the smaller standard deviation.
2. Step 2: Compare the two classes' values of that measureClass A's is smaller.
3. Step 3: So the answer isClass A.
Question 3Work them out, then compare
The numbers of books read by some students in two classes are shown. Class $A$ : $8, \ 20, \ 11, \ 18, \ 13$ . Class $B$ : $27, \ 29, \ 28, \ 26, \ 30$ . Which class read more books on average?
Show the worked solution
1. Step 1: Which measure answers the question?Better on average means the higher mean.
2. Step 2: Work out that measure for each class $A: 14$ $B: 28$
3. Step 3: Compare the two classes' values of that measureClass A's is lower.
4. Step 4: So the answer isClass B.
Question 4Work them out, then compare
The numbers of books read by some students in two classes are shown. Class $A$ : $25, \ 30, \ 28, \ 22, \ 35$ . Class $B$ : $5, \ 9, \ 7, \ 6, \ 8$ . Which class's numbers of books read were more consistent?
Show the worked solution
1. Step 1: Which measure answers the question?More consistent means less spread: the smaller standard deviation.
2. Step 2: Work out that measure for each class $A: 4.43$ $B: 1.41$
3. Step 3: Compare the two classes' values of that measureClass A's is larger.
4. Step 4: So the answer isClass B.

More on statistics

Notes: Statistics Worksheet with answers (PDF)

Endless questions on comparing two data sets

A free account gives you new questions every time, step-by-step help, and tracks what you've mastered.

Start free

Worked example

In a test, class

A

had a mean of

71

marks and a standard deviation of

11.5

marks. Class

B

had a mean of

68

marks and a standard deviation of

10.2

marks. Which class's results were more consistent?

Step 1 of 3

Which measure answers the question?

More consistent means less spread: the smaller standard deviation.

Questions

Question 1Compare by mean and sd

In a test, class $A$ had a mean of $62$ marks and a standard deviation of $6.3$ marks. Class $B$ had a mean of $65$ marks and a standard deviation of $7.9$ marks. Which class did better on average?

Show the worked solution

Step 1: Which measure answers the question?Better on average means the higher mean.
Step 2: Compare the two classes' values of that measureClass A's is lower.
Step 3: So the answer isClass B.

Question 2Compare by mean and sd

In a test, class $A$ had a mean of $62$ marks and a standard deviation of $8.4$ marks. Class $B$ had a mean of $65$ marks and a standard deviation of $12.1$ marks. Which class's results were more consistent?

Show the worked solution

Step 1: Which measure answers the question?More consistent means less spread: the smaller standard deviation.
Step 2: Compare the two classes' values of that measureClass A's is smaller.
Step 3: So the answer isClass A.

Question 3Work them out, then compare

The numbers of books read by some students in two classes are shown. Class $A$ : $8, \ 20, \ 11, \ 18, \ 13$ . Class $B$ : $27, \ 29, \ 28, \ 26, \ 30$ . Which class read more books on average?

Show the worked solution

Step 1: Which measure answers the question?Better on average means the higher mean.
Step 2: Work out that measure for each class $A: 14$ $B: 28$
Step 3: Compare the two classes' values of that measureClass A's is lower.
Step 4: So the answer isClass B.

Question 4Work them out, then compare

The numbers of books read by some students in two classes are shown. Class $A$ : $25, \ 30, \ 28, \ 22, \ 35$ . Class $B$ : $5, \ 9, \ 7, \ 6, \ 8$ . Which class's numbers of books read were more consistent?

Show the worked solution

Step 1: Which measure answers the question?More consistent means less spread: the smaller standard deviation.
Step 2: Work out that measure for each class $A: 4.43$ $B: 1.41$
Step 3: Compare the two classes' values of that measureClass A's is larger.
Step 4: So the answer isClass B.