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प्रश्न
A wall clock strikes the bell once at 1 o’clock, 2 times at 2 o’clock, 3 times at 3 o’clock and so on. How many times will it strike in a particular day? Find the standard deviation of the number of strikes the bell make a day.
उत्तर
Wall clock strikes the bell in 12 hours
1, 2, 3, 4, 5, …, 12
Wall clock strikes in a day ...(24 hours)
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24.
Assumed mean = 14
| xi | di = xi − A = xi − 14 |
di2 |
| 2 | 12 | 144 |
| 4 | − 10 | 100 |
| 6 | − 8 | 64 |
| 8 | − 6 | 36 |
| 10 | − 4 | 16 |
| 12 | − 2 | 4 |
| 14 | 0 | 0 |
| 16 | 2 | 4 |
| 18 | 4 | 16 |
| 20 | 6 | 36 |
| 22 | 8 | 64 |
| 24 | 10 | 100 |
| n = 12 | `sum"d"_"i"` = − 12 | `sum"d"_"i"^2` = 584 |
Here n = 12, `sum"d"_"i"` = − 12, `sum"d"_"i"^2` = 584
Standard deviation = `sqrt((sum"d"_"i"^2)/"n" - ((sum"d"_"i")/"n")^2`
= `sqrt(584/12 - (- 12/12)^2`
= `sqrt(48.67 - 1)`
= `sqrt(47.67)`
= 6.904
= 6.9
Standard deviation of the bell strike in a day = 6.9
Aliter:
A wall clock strikes in a day is 2, 4, 6, 8, 10, 12, ..., 24
2 [1 + 2 + 3 + 4 + 5 ... + 12]
Standard deviation for "n" natural number is (S.D.)
= `sqrt(("n"^2 - 1)/12)`
= `2sqrt((12^2 - 1)/12)`
= `2sqrt((144 - 1)/12)`
= `2sqrt(11.9166)`
= 2 × 3.45
= 6.9
The standard deviation of bell strike in a day is 6.9
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