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Find the arithmetic mean of the given frequency distribution.
| Marks | Frequency |
|---|---|
| 50 | 3 |
| 28 | 4 |
| 85 | 6 |
| 40 | 7 |
56.2
50.5
52.6
40.95
52.6
Calculate the sum of products ∑fixi=(50×3)+(28×4)+(85×6)+(40×7)=150+112+510+280=1052. Divide by the total frequency ∑fi=3+4+6+7=20. Result is 1052/20=52.6.
Data table with Marks (xi): 50, 28, 85, 40 and corresponding Frequencies (fi): 3, 4, 6, 7.
Mean(x)=∑fi∑fixi
Calculate the sum of products ∑fixi=(50×3)+(28×4)+(85×6)+(40×7)=150+112+510+280=1052. Divide by the total frequency ∑fi=3+4+6+7=20. Result is 1052/20=52.6.
Students often make arithmetic errors in multiplication or incorrectly sum the frequencies (fi) which leads to a wrong average.
Calculate the sum of the products (fixi)
Find the product of each mark and its frequency: 50×3=150, 28×4=112, 85×6=510, and 40×7=280. Summing these values gives 150+112+510+280=1052.
∑fixi=1052
Calculate the sum of the frequencies (fi)
Add all frequencies provided in the table: 3+4+6+7=20.
∑fi=20
Calculate the Arithmetic Mean
Divide the sum of the products by the sum of frequencies: x=1052/20=52.6.
x=201052=52.6
C is correct because the calculated arithmetic mean of the frequency distribution is 52.6.
This concept is fundamental for statistics and data interpretation questions where you must always ensure the sum of frequencies matches the denominator in your mean formula.
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