### About Quartiles and five number summary in statistics

**Quartiles and Five-Number Summary**

Another way to look at the variation or spread of the data is to divide the data set up into quartiles. To do this you must first put the data in ascending order.

The middle number of the data set (we know currently as the median) is the middle quartile or second quartile, often written Q2.

To find the first or lower quartile Q1 take the middle number to the left of the median (not including the median). As with the median if you have an odd quantity of values take the two middle values, add them and divide by 2. This will be your lower quartile.

To find the third or upper quartile Q3, take the middle number to the right of the median (not including the median). As with the median if you have an odd quantity of values take the two middle values, add them and divide by 2. This will be your upper quartile.

A five-number summary of a set of data consists of the following information

1. lowest value

2. lower quartile

3. median

4. upper quartile

5. highest value

**Box and Whisker**

A box plot is a graph or picture of the 5 number summary. To draw a box

1. Draw a number line that encompasses all the data values

2. Enclose in a box starting from the lower quartile to the higher quartile

3. Draw a line through the median

4. Add lines from the box (known as whiskers) to the lowest value and the highest value

You should try several of these by hand.

These can also be done on your calculator and using statcrunch.

The first quartile is also known as the 25th percentile. This means 25% of the data is below that data point and 75% is above. The 2nd quartile is known as the 50th percentile (the median) 50% of the data is above the data point and 50% is below. The 3rd quartile is known as the 75th percentile. 75% of the data falls below this point and 25% is above.

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