Comparison of Data Sets (SQA National 5 Maths): Revision Note
Exam code: X847 75
Comparing data sets
How do I compare two data sets?
You may be given two sets of data that relate to a context
To compare data sets, you need to
compare their averages
mean or median
compare their spreads
standard deviation or interquartile range
Examiner Tips and Tricks
You will always compare
either the mean and standard deviation of two sets of data
or the median and interquartile range of the data sets
You should not use the mean with the interquartile range, or the median with the standard deviation.
How do I write a conclusion when comparing two data sets?
When comparing averages and spreads, you need to compare the then
describe what this means in the real life context of the question
Copy the exact wording from the question in your answer
There should be two parts to your conclusion
For example, if class A had a median score of 45 and IQR of 5, and class B had a median score of 32 and an IQR of 12:
"On average class A performed better than class B on the test."
(Because class A had a higher median)
"The scores in class A were less varied than scores in class B."
(Because class A had a smaller IQR)
Other good phrases for lower measures of spread include:
"scores are more consistent"
"scores are closer together"
"scores are less spread out"
Worked Example
A teacher recorded the number of correct answers achieved by a sample of seven students in a short mathematics test.
For School A the mean number of correct answers was 20 and the standard deviation was 3.4.
A sample of students from School B sat the same test. Their results gave a mean number of correct answers of 23 and a standard deviation of 1.5.
Make two valid comments comparing the number of correct answers achieved by the students in School A and School B.
Answer:
Compare the averages
The mean was lower for School A than for school B
On average the number of correct answers was lower in School A than it was in School B
Compare the spreads
The standard deviation was higher for School A than for school B
The numbers of correct answers were more varied in School A than they were in School B
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