Investigate the effect of individual data values including outliers, on the range, mean and median (VCMSP300)
LO: To identify the effects of an outlier on the measures of centrality of a data set.
Know:

What an outlier/outlying value is.

How to calculate the mean of a set of data.

How to calculate the median of a set of data.

How to calculate the mode of a set of data.

How to calculate the range of a set of data.
Understand:

That outliers can sometimes cause issues to the interpretation of collected data and that the removal of outliers helps us to get a more accurate representation of a data set.
Do:

I can identify the effect of outliers to a set of collected data.
Elaborations

using displays of data to explore and investigate effects

exploring the effect of outliers on the range for different sets of data by comparing its value with and without outliers included

determine, through investigation, the effect on a measure of central tendency (i.e., mean, median, and mode) of adding or removing a value or values (e.g., changing the value of an outlier may have a significant effect on the mean but no effect on the median.
Outliers
Outliers or outlying values is data which don’t fit the general trend. They tend to be away from where the majority of the data lies.
Effect of Outliers on Data
Outliers can skew data especially the mean and median from a data set.
If you look at the effects below, without outliers the mean of the data set would have been 3. If you have outlying data with a value of 10, it suddenly changed the mean to 4. In this case the mean didn’t shift that much as it only shifted from 3 to 4.
But if you look in the second scenario, you have the same data set but with 300 as an outlier. The mean shifted from 5.45 to 30, which is a huge shift.
So 1 outlying value can have significant changes to the mean (average) of a data set.
Teaching Ideas

Use a set of data whose distribution across its range looks symmetrical, and change some of the values so that the distribution no longer looks symmetrical. Does the change affect the median more than the mean? Explain your thinking.