Maths- Statistics And Probability

The data set shows a group of continuous data.

This data is called continuous because the scale of measurement - distance - has meaning at all points between the numbers given, eg we can travel a distance of 1.2 and 1.85 and even 1.632 miles.

Continuous data can be shown on a number line, and all points on the line have meaning and are different, but with discrete data only certain values have meaning.

Length of journey to work

Distance in miles 0.1 0.2 0.6 1.1 1.2 1.8 2.0 2.7 3.4 4.6 6.2 8.0 12.1 14.2

This data set shows a group of discretedata.

This is called discrete data because the units of measurement (for example, CDs) cannot be split up; there is nothing between 1 CD and 2 CDs.

Bitesize CD store 31 January 2008

Music format   Number sold

CD albums     140

CD singles      70 Downloads

55 Vinyl          5

Total sales      270

We know that the median divides the data into two halves. We also know that for a set of n ordered numbers the median is the (n + 1) ÷ 2 ^th value.

Similarly, the lower quartile divides the bottom half of the data into two halves, and the upper quartile also divides the upper half of the data into two halves.

Lower quartile is the (n + 1) ÷ 4 ^th value.

Upper quartile is the 3 (n + 1) ÷ 4 ^th value.

The cumulative frequency is obtained by adding up the frequencies as you go along, to give a 'running total'.

Length   Frequency     Cumulative Frequency

21-24     3                   3

25-28     7                  10 (= 3 + 7)

29-32     12                 22 (= 3 + 7 + 12)

33-36     6                   28 (= 3 + 7 + 12 + 6)

37-40     4                   32 (= 3 + 7 + 12 + 6 + 4)

A box and whisker plot is used to display information about the range, the median and the quartiles. It is usually drawn alongside a number line, as shown: