# 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*

- Questions must be specific.
- 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:**

*Reading Pie Charts*

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

*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*

- Cumulative frequency simply means adding the frequencies up as you go along.
- When plotting the graph, always plot points using the
**upper value**of each group. - Cumulative frequency is always plotted on the vertical axis (up the side) and the range of data goes across the bottom.
- 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.

**Median**- go halfway up the cumulative frequency axis, read across and down then read the median from the**bottom scale**.**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**.**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**.**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.