Here is a grouped frequency table.
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Work out an estimate of the mean value.
How to approach this question
1. Add a new column to the table for 'Midpoint × Frequency'.
2. For each row, calculate the product of the midpoint and the frequency.
3. Sum the values in this new column.
4. Sum the frequencies (the total is given as 60).
5. Divide the total of the 'Midpoint × Frequency' column by the total frequency.
Full Answer
The mean of a set of data is the sum of the values divided by the number of values. For grouped data, we don't know the exact values, so we use the midpoint of each group as an estimate for all the values in that group.
First, we find the product of the midpoint and frequency for each group:
5 × 16 = 80
15 × 22 = 330
25 × 13 = 325
35 × 9 = 315
Next, we sum these products: 80 + 330 + 325 + 315 = 1050. This is our estimate for the total sum of all values.
The total number of values is the sum of the frequencies, which is 60.
Finally, we divide the total sum by the number of values: 1050 ÷ 60 = 17.5.
Common mistakes
✗ Dividing the sum of midpoints by the number of groups ( (5+15+25+35)/4 ). This ignores the frequencies.
✗ Dividing the sum of (midpoint × frequency) by 4 instead of the total frequency.
✗ Making calculation errors when multiplying or adding.
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