1. Why do we do statistics?
To Make Inferences from a Small number of cases to a Large number of cases
This means that we have to collect data.

2. Kinds of Data
There are four basic kinds of scores that can be collected.
Nominal
Ordinal
Interval
Ratio
They are known as different types of scales

3. Nominal and Ordinal Scales
Nominal/Categorical Scales
Here numbers are used to divide different behaviours into different classes without implying that the different classes are numerically related to each other.
Ordinal/Ranking Scales
Here numbers are used to indicate a relative position of something in a list. Although we can decide what appears where on a list, in other words the order of the list, we cannot conclude that each item on the list appear at equal intervals.

4. Ratio & Interval Scales
With interval scales we can take a step further than we could with ordinal scales. Interval scales mean that each increase in unit value is one more than the previous value.
Ratio Scales
Although interval scales are useful it is sometimes important to use ratio scales. This is where there are equal intervals with an absolute zero value. Making statements about "A has twice as much x as B" sensible.

5. Describing Data Measure of Central Tendency Measures of Spread
Measures of Form

6. Measures of Central Tendency
There are three commonly used measures of central tendency:
the mode
the median
the arithmetic mean.

7. The Mode
The mode is the score, or the score interval that occurs most frequently in the data.

8. The Median
The median is the score that's at the centre of a distribution of data in the sense that one half of the data values are less than the median, and one half are greater than the median
So with the following data we obtain.
The number that sits exactly in the middle is 46.
So half the numbers (17, 23, 45) are below the median and half the numbers ( ) are above the median

9. The Arithmetic Mean
The arithmetic mean is nothing more than all of the scores added up and divided by the number of scores in the data set.
The formula is normally given as:
So the mean values of the numbers
comes to
/7 = 56.8

10. Properties of the Measures of Centre
All the measure of the centre have two important properties.
Adding or subtracting a constant does the same thing to the measure of centre
Multiplying or dividing by a constant does the same thing to the measure of centre

11. Properties of the Measures of Centre
Of the measures the mode is the only one that is appropriate to use with category or nominal data.
The median is especially useful for ordinal data but is occasionally used with interval and ratio data as well.
The arithmetic mean requires arithmetic operations on intervals between values. For that reason it is only meaningfully used with data that have equal intervals, i.e. data collected using interval and ratio scales

12. Why Look at Measures of Spread and Form?
More scores to the right of your score though your score and the class means are the same
Even more scores to the right of your score though your score and the class means are the same

13. Measures of Spread Distance based measures include: The range
The interquartile range
Centre based measures include:
The variance
The standard deviation.

14. Distance Based Measures of Spread
Range = Largest Value - Smallest Value
Interquartile= Largest Value - Smallest Value after the top and bottom 25% of the distribution is removed

15. Centre Based Measures of Spread
Several statistics use the centre of the data as a point of reference and reflect how data clustered around it.
Of these, the variance and the standard deviation are the most widely used.
Both of which are based on the arithmetic mean.

16. Variance The variance of a set of scores is defined as:
As the spread in a set of scores increases so does the variance.

17. Standard deviation
The standard deviation of a set of scores is defined as:
As the spread in a set of scores increases so does the standard deviation.
The standard deviation is on the same scale as the original set of scores.

18. Using Measures of Centre and Spread
Nominal
Mode
Ordinal
Median
Range, Interquartile Range
Interval/Ratio
Mode, Median, Mean
Range, Interquartile Range, Variance, Standard Deviation

19. Measures of Form
The Normal Distribution
Skew
Kurtosis

20. The Normal Distribution

21. Skew
Positive Skew
Negative Skew

22. Kurtosis
Leptokurtosis
Platykurtosis