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Measures of average

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Mean and modal class

Calculating the mean and modal class for grouped data is very similar to finding the mean from an ungrouped frequency table, except that you do not have all the information about the data within the groups so can only estimate the mean.

Calculating the mean from grouped data

Example

Question

This table shows the weights of children in a class.
Using this information:

a) Estimate the mean weight
b) Find the modal class

Mass (m) kg Frequency
30 ≤ m < 40 7
40 ≤ m < 50 6
50 ≤ m < 60 8
60 ≤ m < 70 4
Answer

To estimate the mean weight, you know that 7 children are between 30kg and 40kg, but you don't know exactly how much they weigh, so assume that they all weigh 35kg (the midpoint of the group).

Do the same for all the other groups:

Mass (m) kg Midpoint Frequency Midpoint × Frequency
30 ≤ m < 40 35 7 245
40 ≤ m < 50 45 6 270
50 ≤ m < 60 55 8 440
60 ≤ m < 70 65 4 260
  Totals 25 1215

a) Estimate of mean = 1215 ÷ 25 = 48.6 kg

b) The modal class is the class that has the highest frequency. In this case the modal class is 50 ≤ m < 60

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