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# Measures of spread

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## Measures of spread

Where the **median **gives us the mid-value of our data, the **lower quartile** gives us the value of the lowest quarter and the **upper quartile** gives us the value of the highest quarter.

The **inter-quartile** range is the **difference** between the upper and lower quartiles and gives us the middle half of our data.

To find the values of these quartiles depends on whether you have an even or odd number of pieces of data (exactly like the median).

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The **standard deviation** gives a measure of how the data is dispersed about the mean, the centre of the data. This gives us a kind of measure of the spread of our data - the lower the standard deviation, the more compact our data is around the mean. It's extremely useful when comparing 2 sets of data.

There are 2 formulae for calculating the standard deviation,

**Formula 1:**

**Formula 2:**

They may look pretty complicated, but in fact are pretty easy to use, especially the second one which is the more widely used.

**Example: **

To find the standard deviation of this set of numbers:

We will need the mean to calculate the standard deviation where:

**...obviously both giving the same result. **

The quickest method of all however, is to put the data into your calculator and let that do all the work for you! If you have an **sd** mode on your calculator you will be able to do this. You will need to read for yourself or ask a teacher as all calculators are slightly different. Most exam questions will involve larger sets of data and most of the time you will be given summarised data to calculate from.

Most exam questions will involve larger sets of data and most of the time you will be given summarised data to calculate from.

**The variance is the square of the standard deviation.**

Variance = σ^{2}

This gets rid of the square root sign in the 2 formulae used above. The varianceis used a lot in later work on statistics.