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प्रश्न
Compute the mean from the following data:
| Marks | 0 – 7 | 7 – 14 | 14 – 21 | 21 – 28 | 28 – 35 | 35 – 42 | 42 – 49 |
| Number of students | 3 | 4 | 7 | 11 | 0 | 16 | 9 |
योग
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उत्तर
1. Construct the cumulative frequency table
| Marks (Class Interval) |
Number of Students (f) |
Cumulative Frequency (cf) |
| 0 – 7 | 3 | 3 |
| 7 – 14 | 4 | 7 |
| 14 – 21 | 7 | 14 |
| 21 – 28 | 11 | 25 |
| 28 – 35 | 0 | 25 |
| 35 – 42 | 16 | 41 |
| 42 – 49 | 9 | 50 |
| Total (N) | 50 |
2. Identify the median class
Total frequency (N): 50
`N/2` value: `50/2 = 25`
Look at the cumulative frequency (cf) column to find the first class where the cumulative frequency is greater than or equal to 25.
The class 21 – 28 has a cumulative frequency of exactly 25. Therefore, 21 – 28 is the median class.
3. Apply the median formula
Medain = `L + ((N/2 - cf)/f)`
Where:
L (Lower limit of the median class) = 21
cf (Cumulative frequency of the preceding class) = 14
f (Frequency of the median class) = 11
h (Class width/size) = 7
Substitute these values into the formula:
Median = `21 + ((25 - 14)/11 xx 7)`
Medain = `21 + (11/11) xx 7`
Median = 21 + 1 × 7
Median = 21 + 7 = 28
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