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प्रश्न
Complete the following activity to find median.
| Class (Student's marks) |
No. of students fi |
Cumulative frequency less than the upper limit cf |
| 0 – 20 | 4 | 4 |
| 20 – 40 | 20 | 24 |
| 40 – 60 | 30 | 54 |
| 60 – 80 | 40 | 94 |
| 80 – 100 | 6 | 100 |
Here, L = `square`, N = 100, `N/2 = 50`, c.f. = 24, f = 30, h = 20
Median = `square` ...(Formula)
= `square`
Median marks = `square`
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उत्तर
Step 1: Find the missing parameters
From the given data, since `N/2 = 50`, the cumulative frequency just greater than 50 is 54.
This corresponds to the median class of 40 – 60.
L (Lower limit of the median class) = \[\boxed{40}\]
Step 2: Formula and Calculation
Substitute the values into the median formula:
Medain = \[\boxed{L + \left[{\frac{\frac{N}{2}-c.f.}{f}}\right] \times h}\]
Substituting the given values (L = 40, `N/2 = 50`, c.f. = 24, f = 30, h = 20):
Median = \[\boxed{40 + \left[{\frac{50 - 24}{30}}\right] \times 20}\]
Median = `40 + [26/30] xx 20`
= `40 + 52/3`
= 40 + 17.33
= \[\boxed{57.33}\]
