Statistics and parameters

To find out about a population we take a sample

Statistics describe features of the sample What statistics do we use? How are they calculated?

We use sample statistics to make inferences about population parameters  Proportion  Central tendency  Variation or spread  Shape  Unusual features

The Measures of Central Tendency The Mean is easy to calculate and is also easily understood. BUT! It is affected by extreme values.

The Measures of Central Tendency The Median is unaffected by extreme values, but it is more difficult to calculate as the data has to be ordered first. BUT! It is UNaffected by extreme values.

The Measures of Central Tendency The Mode is useful to manufacturers who want to identify the most popular value. BUT! It is not always typical of a population as a whole.

The Measures of Central Tendency The Mean is easy to calculate and is understood. BUT! It is affected by extreme values.

The Measures of Spread The Range is the difference between the maximum and minimum values. The range is easy to calculate and understand. BUT! If there are extreme values, the range does not accurately reflect how spread out the data values are.

The Measures of Spread The Inter-quartile Range is the difference between the upper quartiles and the lower quartile and gives the range of the middle 50% of the data. As the extreme values are outside the middle 50% of the data, the inter-quartile range gives a clear indication of the spread.

The Measures of Spread The Standard deviation is a calculated measure of spread which is shows how much variance there is from the mean. You can safely conclude that a set of data with a larger standard deviation is more spread out than a set of data with a smaller standard deviation.