Comparing Distributions and Finding Outliers

2F: Centre and Spread for Symmetric Distributions

Symmetric Distributions

*with no outliers

Centre: Mean or Median

Spread: Standard Deviation

Mean

Mean = (sum of all values) / (number of values)

PADLET

We know that the mean (average) value of a data set is the sum of the values/number of values.

But what does this tell us?

Interpretation of the mean

The mean is the balance point of a distribution

Fill in the Blanks

For the data set: 1, 1, 2, 3, 5, 7

find:

Fill in the Blanks

For the data set: 1, 1, 2, 3, 5, 7

find:

Fill in the Blanks

For the data set: 1, 1, 2, 3, 5, 7

find: (correct to 2 decimal places)

Smart Investment

HOUSE PRICES

https://www.smartpropertyinvestment.com.au/research/13198-investors-misled-by-skewed-median-prices

Multiple Choice

Which types of distribution should be not use the mean for?

• Symmetrical distributions

• Skewed distributions

Open Ended

Why should we not use the mean when describing skewed distributions?

HOUSE PRICES

https://www.jimsparrow.com/blog/average-or-median-sale-price.html

Mean vs Median

The mean is not appropriate for determining the centre of the data for skewed distributions. Why?

Mean is significantly affected by extreme values. The median is a better measure of centre as it is relatively unaffected by the presence of extreme values.

Standard Deviation

standard deviation

To measure the spread of a data distribution around the median (M) we use the interquartile

range (IQR). To measure the spread of a data distribution about the mean ( ¯x) we use the

standard deviation (s).

Fill in the Blanks

The following are the heights (in cm) of a group of women.

176 160 163 157 168 172 173 169

Determine the standard deviation using your CAS