P9 | Maths Made Easy

P9

QUESTION: Below is some data collected on the heights, in cm, of 10 men.

181,\,182,\,175,\,176,\,210,\,169,\,175,\,184,\,167,\,175

a) Find the mean of these data.

b) Find the median of these data.

c) Explain why the median might be a better measure of the average in this case. (Hint: one of these values is different to the others – what difference does it make?)

 

ANSWER: a) We must add up all the values and divide by 10.

\text{mean }=\dfrac{181+182+175+176+210+169+175+184+167+175}{10}=179.4\text{ cm}

b) To find the median, we must first put the values in ascending order:

167,\,169,\,175,\,175,\,175,\,176,\,181,\,182,\,184,\,210

Then, if you cross off alternating biggest and smallest values, you’ll be left with two numbers: 175 and 176. Therefore, the median is 175.5cm, (the halfway point).

c) In this case, the man who is 210cm tall is significantly taller than the other men. Therefore, when we calculate the mean, the 210 value is going to make the mean much higher than otherwise, and it might not be representative of the data (try calculating the mean without 210 and see what happens). The median, however, is not affected by the value of 210, so it might be a better measure of average in this case.