Mode-Median-And-Mean gcse Edexcel

Mode, Median & Mean from Discrete Data

Why do we have different types of average?

• You’ll hear the phrase “on average” used a lot

  • For example

    • by politicians talking about the economy

    • by sports analysts

• However not all data is numerical

  • e.g. the party people voted for in the last election

• And even when data is numerical

  • some of the data may lead to misleading results

• This is why we have 3 types of average

What are the three types of average?

1. Mean

• This is what people usually mean when they say “average”

  • In an ideal world where everybody had the same amount of some resource

  • the mean is the amount of that resource that each person would have

• It is also known as the arithmetic mean

• It is the total of all the values divided by the number of values

  • 

    • i.e. add up all the data values

    • then divide by how many values there are

• Problems with the mean occur when there are one or two unusually high (or low) values in the data (outliers)

  • These can make the mean too high (or too low) to accurately represent any patterns in the data 

2. Median

• This is similar to the word medium, which can mean ‘in the middle’

• So the median is the middle value

  • But beware, the data has to be arranged into numerical order first!

• Use the median instead of the mean if you don’t want extreme values (outliers) affecting the average

• If there are an odd number of values, there will only be one middle value

  • This will be the ^th value

    • e.g. for 35 data values, and

    • So the median will be the 18^th value

• If there are an even number of values there will be two values in the middle

  • In this case we take the halfway point between these two values

  • Often the halfway point is obvious

  • If not, add the two middle values and divide by 2

    • this is the same as finding the mean of the two middle values

3. Mode

• Think of MOde as meaning the Most Often

  • i.e. it is the value that occurs the greatest number of times

• It is often used for things like “favourite …” or “… sold the most” or “… were the most popular”

• Not all data is numerical and that is where the mode is especially useful

  • But be aware that the mode can be applied to numerical data

    • e.g. data about sales of clothing or shoes in different sizes

    • mode would be the best average for determining demand for the sizes

• The mode is sometimes referred to using the word modal

  • e.g. you may see a phrase like “modal value”

  • This means the same thing, the value occurring most often

• Sometimes no value occurs more often than any other

  • In this case we say there is no mode

• If two values occur most often we may say there are two modes

  • or say that the data set is bi-modal

  • Whether it is appropriate to do this will depend on what the data is about

How do changes in the data affect the average?

• You should be able to determine how a change in the data can affect the mean, median or mode

  • For example adding or removing data values to the set

• You can always recalculate the averages using the changed data set

  • This may be necessary if you need the exact values of the new averages

• But sometimes you can use logic to decide what kind of change will occur

• For the mode

  • If an added data value is equal to the modal value, it will not change the mode

  • If a removed data value is not equal to the modal value, it will not change the mode

  • Otherwise recalculate

• For the mean

  • If an added data value is

    • greater than the mean, the mean will increase

    • less than the mean, the mean will decrease

  • If a removed data value is

    • greater than the mean, the mean will decrease

    • less than the mean, the mean will increase

  • (If an added or removed data value is equal to the mean, the mean will not change!)

  • Recalculate to find the exact value of a changed mean

• For the median

  • You will need to examine the changed data set to decide if the median has changed

  • Make sure the values in the changed set are written in order!