# Interpreting Data

## Interpreting Graphs

When it comes to interpreting graphs we can tell a lot about the data, and the spread of the data just by looking at the graphs.

**Histograms**

Below are two histograms showing the weight of plant type a and plant type b.

Plant type a shows a **high dispersion- a large spread of results away from the mean**. It shows that the results are not close together there is a lot of variation within the data.

Plant type b shows a **distribution that is closer to the mean**, this means that most of the results are within a narrow range, there is less variation within the data.

**Analysing the Cumulative Frequency Curve**

To analyse the cumulative frequency curve think about how it relates to the interquartile range.

The steeper the curves will show a small interquartile range, whilst gentler gradients indicate a wider interquartile range.

Eg. The purple curve is alot steeper and has a very small interquartile range which means the values in the data are close the the median. Whilst the green curve has a larger interquartile range which means the values are more evenly distributed.

## Analysing box plots

When it comes to box plots we are able to visually see the difference in spreads between data sets.

When analysing a box plot make sure you compare:

- The interquartile range
- The median

For example if you wanted to compare these box plots it would be worth mentioning:

**Boxplot A:**

- Has a symmetrical lower and upper quartile because the median is exactly in the middle of the box.
- The interquartile range is small, which tells us that there is not a large spread between the data points.

**Boxplot B:**

- Has a large interquartile range which means there is a large spread of the data.
- The median is closer to the upper quartile than the lower quartile.

**Boxplot C:**

- The interquartile range shows that most of the data is close to the highest value.
- The median is closer to the lower quartile than the higher quartile

- How do you work out the interquartile range?
- Your answer should include: Upper Quartile / Lower Quartile
- What does a large range tell you about a set of data?
- Spread

## Measures of central tendency

To analyse graphs (and data more generally) you want to look at:

- The averages (mode, mean and median)
- The spread of the data (the range and the interquartile range)

The **averages or measures** of central tendency tell you different things about the data:

**Mode**: This tells you the most common or most frequent data point (look for the most frequent value).**Median**: This tells you the middle point in the data (imagine lining things up in size order and picking the middle value)**Mean**: This takes into account all the data points and gives you an average of those points. (Total Total number of things). Take care with the mean- if you have a couple of points that are very high or very low, this can have a large impact on the mean!

Measures of spread:

**The Range**: Biggest value- smallest value

This tells you the difference between the highest value and the lowest value. It tells you how spread out the data is. Therefore if you have a large range it means that there is a big difference between the highest and lowest value.

**The Interquartile range**: This tells you about the range within 75% of the data. It discounts the highest quarter and the lowest quarter. This means it tells you more about how the data around the median is spread.

- What does a large range tell you about a set of data?
- Spread Out
- How do you work out the interquartile range?
- Your answer should include: Upper Quartile / Lower Quartile
- What two things should you compare when looking at boxplots:
- Your answer should include: Interquartile Range / Median