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प्रश्न
The mean of the following data is 16. Calculate the value of f:
| Marks | 5 | 10 | 15 | 20 | 25 |
| No. of students | 3 | 7 | f | 9 | 6 |
बेरीज
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उत्तर
1. Organize the data
First, let’s set up a table to calculate the total number of students and the sum of all marks.
| Marks (x) | No. of students (f) | f × x |
| 5 | 3 | 15 |
| 10 | 7 | 70 |
| 15 | f | 15f |
| 20 | 9 | 180 |
| 25 | 6 | 150 |
| Total | Σf = 25 + f | Σfx = 415 + 15f |
2. Apply the mean formula
The formula for the mean `(barx)` is:
`barx = (sum(f xx x))/(sumf)`
Given that the mean is 16, we can plug in our values:
`16 = (415 + 15f)/(25 + f)`
3. Solve for f
Now, we use algebra to find the missing frequency:
1. Multiply both sides by (25 + f):
16(25 + f) = 415 + 15f
2. Expand the left side:
400 + 16f = 415 + 15f
3. Rearrange to group f terms on one side:
16f – 15f = 415 – 400
4. Simplify:
f = 15
The value of f is 15.
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