## Representing Data

## Stem and Leaf Diagram

Used to display a simple list

## Box Plot

## Outlier

An outlier is a value that is so out of trend it is not considered a true representation of the data

The outliers are

The outliers are

**1.5 x IQR above Q3 or 1.5 x IQR below Q1**## Histogram

The histogram gives a general shape for the data.

Is used instead of a bar chart as a a bar chart can't used grouped data with differing class widths

Is used instead of a bar chart as a a bar chart can't used grouped data with differing class widths

__frequency__= frequency density**class width**

**The area of the bars gives the frequency**

*Skewness*

In box plots and histograms the correlation can't be discussed (that comes in correlation)

Instead the skewness of the data is discussed

Instead the skewness of the data is discussed

In an exam they'll give you a

E.g.

standard deviation

If the value is

If the value is

If the value is

You may get asked to give further explanation to your skewness coefficient.

For this say

(if a positive skew) The

(if normal distribution) The

(if a negative skew) The

**equation**that works out the**skewness coefficient**.E.g.

__3(mean - median)__standard deviation

If the value is

**positive**then it's a**positive skew**If the value is

**around 0**then it's a**normal distribution**If the value is

**negative**then it's a**negative skew**You may get asked to give further explanation to your skewness coefficient.

For this say

(if a positive skew) The

**mean > median > mode**(if normal distribution) The

**mean = median = mode**(if a negative skew) The

**mean < median < mode***This may be worth four marks*## Comparing

When comparing two sets of data use common sense.

Compare the:

Use whatever data you are given or have worked out

Compare the:

- skewness
- range
- averages
- IQR
- standard deviation

Use whatever data you are given or have worked out