Mode & Mean from Grouped Data (Edexcel GCSE Statistics)

Mode & Mean from Grouped Data

How do I estimate the mean for grouped data?

• It is impossible to find the mean for grouped data, because we don't have access to the original data values

  • i.e. there is no way to find the exact sum of all the data values

  • so we can't use the formula

• However we can estimate the mean for grouped data

  • To do this we use the class midpoints as our data values

    • e.g. if a class interval is 150 ≤ x < 160

    • we assume that all the data values are equal to the midpoint, 155

• STEP 1
  Draw an extra two columns on the end of a table of the grouped data

  • In the first new column write down the midpoint of each class interval

  • If the midpoint isn't obvious, add the endpoints and divide by 2

    • e.g. if a class interval is 150 ≤ x < 160

    • the midpoint is

• STEP 2
  Calculate "frequency" × "midpoint" (this is often called fx)

  • Write these values in the second column you added to the table

• STEP 3
  Total the fx column and (if necessary) the frequency column

  • The question may already tell you the total number of data values (i.e. the total frequency)

    • In that case there's no need to find the total of the frequency column

• STEP 4
  Estimate the mean by using the formula

  • 

    • i.e. divide the total of the fx column by the total number of data values

How do I find the modal class?

• It is impossible to find the modal value (i.e. mode) for grouped data, because we don't have access to the original data values

  • i.e. it is impossible to say which value occurs the most times

• For grouped data we talk about the modal class instead

  • This is the class with the highest frequency

    • Just find the highest frequency in the table

    • The corresponding class interval tells you the modal class

• Be careful not to confuse the modal class with its frequency

  • e.g. if the highest frequency in the table is 34, corresponding to the class interval

    • then the modal class is

    • The modal class is not '34'!

What if the grouped data is in a histogram?

• Remember that a histogram is a way of presenting grouped data as a diagram

• To estimate the mean or find the modal class it will usually be easiest to rewrite the data as a table first

  • The class intervals can be read off the horizontal axis

  • You may need to calculate the frequencies using
    

• If the class widths are equal then the modal class will be the one with the highest bar on the histogram

  • But for unequal class widths you need to calculate the frequencies to determine the modal class