Dishonest Teacher

Introduction

In this lesson, you will learn that statistics can sometimes be manipulated to mislead people!

Look at the table on the right, work out the mean, mode, median and range for each class.

Which class is the best? Which class is the worst? Justify your answers.

A dishonest teacher thinks that some of the averages look a bit low. Then he has an idea. ‘If I take pupil 5 out of class A and put him in class B, I wonder what would happen to the mean scores?’

What will happen to the mean score in class A?
What will happen to the mean score in class B?

You may wish to make a copy of this spreadsheet to help speed the calculations up.

Dishonest Teacher - Data v2 with Mode Median.xlsx

Further Questions and Challenges

Which other pupils could be moved without reducing any of the means?

What do you think is the 'best' set of averages he can obtain by shifting pupils around? Why?

What is the highest mean of means? What about the lowest?

Can all classes get over 60%? Why/ why not?

Extension

Here is a set of data for Mr John and Ms Helen's classes.

What calculations can/ should you do with the data?
What conclusions can you make? Hint: if you are not sure, take a look at the questions on the sheet for some clues.
Can you manipulate the data so that both classes have the same mean? Why/ why not?
- You may wish to make a copy of this spreadsheet to help speed the calculations up - you will have to change it, can you work out how?

Take a look at this video of misleading statistics in advertising and the news. Here are more examples.

Comparing Graphs - would you recognise a misleading graph if you saw one? Try this comparative judgement exercise to rate statistical graphs.