NZ Level 8 (NZC) Level 3 (NCEA) [In development]

Central Tendency Suitability

Lesson

There are three measures of central tendency that you will need to consider - mean, median and mode.

When deciding which to use you need to remember that the whole data set should be represented by whichever measure you choose. There are two main things you should look out for. The first is a repeated value. If the same data point keeps coming up, it is probably a good representation of the whole data set. This would suggest the mode is the best measure of centre to use.

The second thing you should look out for is an outlier. An outlier is something that is very different to the rest of the data set. For example, if you went to a shop to buy a chocolate bar and found most were around $\$1$$1 but there was one bar that cost $\$20$$20 the expensive bar is an outlier.

So which measure of centre do you choose? The decision tree below should help.

A set of data has a mean of $x$`x`, the outlier is removed and the mean rises. The outlier must have had:

a value, but we cannot tell if it was larger or smaller

Aa value smaller than the values that remain

Ba value larger than the values that remain

Ca value, but we cannot tell if it was larger or smaller

Aa value smaller than the values that remain

Ba value larger than the values that remain

C

A set of data has a mean of $x$`x`, the outlier is removed and the median lowers. The outlier must have had:

a value smaller than the values that remain

Aa value, but we cannot tell if it was larger or smaller

Ba value larger than the values that remain

Ca value smaller than the values that remain

Aa value, but we cannot tell if it was larger or smaller

Ba value larger than the values that remain

C

The number of animal races that were won by a trainer over the years shown are listed in the table.

Year | $2003$2003 | $2004$2004 | $2005$2005 | $2006$2006 | $2007$2007 |
---|---|---|---|---|---|

Races won | $116$116 | $105$105 | $102$102 | $108$108 | $113$113 |

What measure of centre should you use for the data above?

Mean $=$= $108.8$108.8

AMedian $=$= $108$108

BMean $=$= $108.8$108.8

AMedian $=$= $108$108

B

Carry out investigations of phenomena, using the statistical enquiry cycle: A conducting experiments using experimental design principles, conducting surveys, and using existing data sets B finding, using, and assessing appropriate models (including linear regression for bivariate data and additive models for time-series data), seeking explanations, and making predictions C using informed contextual knowledge, exploratory data analysis, and statistical inference D communicating findings and evaluating all stages of the cycle.

Use statistical methods to make a formal inference