Statistics 1 – further mean and standard deviation

Yesterday you should have revised how to find the mean and standard deviation using your calculator. But what would happen to the mean and standard deviation if the data changed. This is what we will look at today. Sadly I can’t find a video so instead I’ll write a brief explanation. Once your happy you understand then take a look at the questions and as normal New College students can get further help at our Facebook Support Group.

For a group of students the mean height is 140 cm with a standard deviation of 20 cm. Supposing the students were incorrectly measured, what would the new mean and standard deviation be if;

1. all the heights were over measured by 1 cm.

In this case only the mean will increase by 1cm to 141 cm. The standard deviation won’t change as the data is not more spread out, just moved up by one.

Similarly the median and quartiles would increase by 1 cm and the range would be unchanged.

2. all the heights should actually be 10% higher.

In this case both the mean and standard deviation should be increased by 10%. This is because adding 10 % to the shortest student won’t increase the height by as much as adding 10% to the tallest student. As a result the data becomes more spread out.

Similarly the quartiles and range will also increase by 10%.

Now have a go at the questions below. You may also need to check the videos below if you’ve forgotten how to find the median and quartiles.