# Interpreting data

## In a nutshell

When given any kind of diagram showing a collection of data, it's important to be able to interpret the information. Diagrams could be misleading, averages could be affected by outliers - there are lots of things that can affect the data.

## Misleading diagrams

### Definition

A misleading diagram is one that gives information in a way that makes it seem like something it isn't.

When drawing your own diagrams to show data, there are set rules that you must follow such as having an equal scale and labelling the axis. It's important to notice when these things are missing so that you can be aware if they are misleading.

##### Example 1

*This line graph is misleading for many reasons. List three things wrong with the graph.*

*1. The 'temperature' axis has an inconsistent scale - it does not go up in equal increments.*

*2. There is no label on the x-axis.*

*3. There is no title - this line graph could be showing anything!*

*This graph shows average temperatures each month. What is misleading about the change in temperature from February to April?*

*The line graph shows a straight line suggesting that the temperature changed evenly each month. However the scale tells us that from February to March there was an increase of *$2\degree C$*, whereas from March to April there was a huge increase of *$20\degree C$*!*

## Outliers resulting in a misleading mean and range

Another thing that can result in misleading information is an outlier - a data value that does not fit the general trend. Since they are far off the rest of the data, they lead to the mean and range becoming much smaller or bigger than they should be.

##### Example 2

*Sarah records the number of books she reads every month for a year. The results are as follows:*

$3,4,2,1,3,20,2,3,4,3,2,1$

*Which value is the outlier?*

*Pick the value that does not seem to fit with the rest.*

$\underline{20}$

*Calculate the mean and average both with and without the outlier.*

**With the outlier**
| **Without outlier** |

**Mean:**
*Add up all the values and divide by the frequency. *
$\frac{3+4+2+1+3+20+2+3+4+3+2+1}{12}=\frac{48}{12}=\underline{ 4}$**
**Range:**
*Minus the smallest value from the largest.* $20-1=\underline{19}$**
| **Mean:**
*Add up all the values and divide by the frequency.* *$\frac{3+4+2+1+3+2+3+4+3+2+1}{11}=\frac{28}{11}=\underline{ 2.55}$ * **
**Range:**
*Minus the smallest value from the largest.* $4-1=\underline3$ |

*Notice how, without the outlier, the mean and range are both much smaller and in fact, much less misleading too.*