HSC Standard Maths Resources

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2.1.1 Sample Data

The easiest way basic statistics can be asked in an exam is by giving you a data set and then asking you to calculate any of the stats mentioned in previous section. Following are the basics you need to know to get yourself started with these:

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Example 1

You are given following set of ten scores in a mathematics test. Answer the questions below:

88, 93, 58, 76, 79, 65, 77, 68, 51, 77

Calculate i) mean, ii) mode, iii) median, iv) lower quartile, v) upper quartile, vi) interquartile range, vii) range, viii) standard deviation.

Things can get little tricky when instead of asking you to calculate these stats directly, examiner asks you to:

– calculate missing value in a data set by giving you a sample data and one of the stats above

– determine effect on a given statistics when new data is added

– compare statistics of two given data sets

The basics of solving all the above remain the same. They are merely an extension of basics with additional layers.

Example 2

A data set of 10 scores has a mean of 15. The scores 10, 12, 15, and 23 are added to this data set. What is the mean of the data set now?

Example 3

A set of data of 9 scores is shown with the first number missing, in ascending order.

?, 3, 5, 8, 9, 12, 15, 18, 22

The range of the data is 21. What is the five-number summary for this data set?

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