Comparison of Data Sets (SQA National 5 Applications of Mathematics): Revision Note
Exam code: X844 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 compare two averages?
Identify which data set has the highest average
Write your comment in context and include the word "average"
e.g. on average, students in class A scored higher on the test than students in class B
e.g. the average hotel price is lower in Edinburgh compared to Glasgow
Make sure your comment is specific
e.g. on average, class A is higher
This has not mentioned that the scores are higher
Do not use the words "average" and "mean" in the same comment
e.g. on average, the mean score of students in class A is higher
This is not a comparison of the data
Examiner Tips and Tricks
Remember, if a data set has a higher average, then it does not automatically mean that it is better. For example, if you are recording the times taken to complete a puzzle, then the lower times are better.
How do I compare two spreads?
Identify which data set has the lowest spread
Write your comment in context and include a word such as "varied", "consistent" or "spread"
e.g. the scores of students in class A are more consistent
e.g. hotel prices in Edinburgh are more varied
Make sure your comment is specific
e.g. the students in class A are more consistent
This has not mentioned that the scores are more consistent
Do not talk about the interquartile range or standard deviation
e.g. the standard deviation for students is class A is higher
This is not a comparison of the data
Examiner Tips and Tricks
If you have to compare both an average and spread within the same question, then write two separate sentences. Otherwise, if you try to combine both comments into one sentence, it might be ambiguous.
For example, the following sentence would only get one out of two marks.
"On average, students in class A scored higher and were more consistent."
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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