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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.
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 |
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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