Advertisements
Advertisements
प्रश्न
The time taken by 50 students to complete a 100-meter race are given below. Find its standard deviation
| Time taken (sec) | 8.5 − 9.5 | 9.5 − 10.5 | 10.5 − 11.5 | 11.5 − 12.5 | 12.5 − 13.5 |
| Number of students | 6 | 8 | 17 | 10 | 9 |
उत्तर
Assumed mean = 11
| Time taken | Number of students fi |
mid value xi |
di = xi − A = xi − 11 |
fidi | fidi2 |
| 8.5 − 9.5 | 6 | 9 | − 2 | − 12 | 24 |
| 9.5 − 10.5 | 8 | 10 | − 1 | − 8 | 8 |
| 10.5 − 11.5 | 17 | 11 | 0 | 0 | 0 |
| 11.5 − 12.5 | 10 | 12 | 1 | 10 | 10 |
| 12.5 − 13.5 | 9 | 13 | 2 | 18 | 36 |
| `sumf_"i"` = 50 | `sumf_"i""d"_"i"` = 8 | `sumf_"i""d"_"i"^2` = 78 |
Here N = 50, `sumf_"i""d"_"i"` = 8, `sumf_"i""d"_"i"^2` = 78
Standard deviation (σ) = `sqrt((sumf_"i""d"_"i"^2)/"N" - ((sumf_"i""d"_"i")/"N")^2`
= `sqrt(78/50 - (8/50)^2`
= `sqrt(1.56 - (0.16)^2`
= `sqrt(1.56 - 0.025)`
= `sqrt(1.56 - 0.03)`
= `sqrt(1.53)`
= 1.236
⇒ 1.24
∴ Standard deviation (σ) = 1.24
APPEARS IN
संबंधित प्रश्न
Find the range and coefficient of range of the following data
43.5, 13.6, 18.9, 38.4, 61.4, 29.8
Calculate the range of the following data.
| Income | 400 − 450 | 450 − 500 | 500 − 550 | 550 − 600 | 600 − 650 |
| Number of workers | 8 | 12 | 30 | 21 | 6 |
Find the variance and standard deviation of the wages of 9 workers given below:
₹ 310, ₹ 290, ₹ 320, ₹ 280, ₹ 300, ₹ 290, ₹ 320, ₹ 310, ₹ 280
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.
Find the standard deviation of the first 21 natural numbers.
If the standard deviation of a data is 4.5 and if each value of the data is decreased by 5, then find the new standard deviation
The measurements of the diameters (in cms) of the plates prepared in a factory are given below. Find the standard deviation
| Diameter (cm) | 21 − 24 | 25 − 28 | 29 − 32 | 33 − 36 | 37 − 40 | 41 − 44 |
| Number of plates | 15 | 18 | 20 | 16 | 8 | 7 |
For a group of 100 candidates, the mean and standard deviation of their marks were found to be 60 and 15 respectively. Later on, it was found that the scores 45 and 72 were wrongly entered as 40 and 27. Find the correct mean and standard deviation
The mean and variance of seven observations are 8 and 16 respectively. If five of these are 2, 4, 10, 12 and 14, then find the remaining two observations.
The frequency distribution is given below.
| x | k | 2k | 3k | 4k | 5k | 6k |
| f | 2 | 1 | 1 | 1 | 1 | 1 |
In the table, k is a positive integer, has a variance of 160. Determine the value of k.
