S-Cool Revision Summary

S-Cool Revision Summary

Gathering data

There are two types of number data: Discrete and Continuous.

Discrete data can only take specific values and not the values in-between.

Continuous data can take any value within your range of accuracy.

Questionnaires

  1. Questions must be specific.
  2. Questions must not be leading.

Analysing Data

Always rearrage the data in ascending order!

Then learn these definitions:

Mean is the total of all the items divided by the number of items.

Median is the middle value.

Mode is the most common value.

Range is the difference between the smallest and the biggest value.

Comparing two sets of data

Either compare their means and their ranges or their medians and their ranges.

Grouped data

Mean - assume all the items in a group take the mid-point of the group so for each group you do mid-point x frequency. Add them all up and divide by the Total Frequency.

Median - you cannot find the median, only the group that it is in.

Modal group - the group with the highest frequency.

Pie charts

Making Pie Charts

To work out the angle needed for each section:

Copyright S-cool

Reading Pie Charts

To find out the frequency that each section represents, measure the angle for the section then:

Copyright S-cool

Frequency Diagrams

These are sometimes called bar charts.

These are a good way of looking at the spread of data and are very easy to draw.

Line Graphs

Line Graphs are only used for discrete data and are simply a line (instead of a bar) for each data value showing total frequency.

Frequency Polygons

Again, these are done in the same way as Frequency Diagrams but you do not draw the bars.

Instead you put a little cross where the middle of the bar would have been then join all the crosses togethere.

Cumulative Frequency

Key Points

  1. Cumulative frequency simply means adding the frequencies up as you go along.
  2. When plotting the graph, always plot points using the upper value of each group.
  3. Cumulative frequency is always plotted on the vertical axis (up the side) and the range of data goes across the bottom.
  4. The shape of a cumulative frequency curve looks like a 'stretched S' and is called an ogive.

The more 'stretched-out' the 'S' is the more spread out the data is. An 'S' with a very steep middle section indicates the data being tightly grouped around the median.

  1. Median - go halfway up the cumulative frequency axis, read across and down then read the median from the bottom scale.
  2. Lower Quartile - go a quarter of the way up the cumulative frequency axis, read across and down then read the Lower Quartile from the bottom scale.
  3. Upper Quartile - go three-quarters of the way up the cumulative frequency axis, read across and down then read the Upper Quartile from the bottom scale.
  4. Inter-Quartile Range - the difference between the Lower Quartile and the Upper Quartile.

Scatter Diagrams

Simply plot crosses on a graph for the two things you are looking at.

If the data follows a 'trend' or 'correlation' we can draw a line of best fit showing the general slope of the data.

You can then get further information from the graph by using your line of best fit.