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
63, 89, 98, 125, 79, 108, 117, 68
A teacher asked the students to complete 60 pages of a record notebook. Eight students have completed only 32, 35, 37, 30, 33, 36, 35 and 37 pages. Find the standard deviation of the pages yet to be completed by them.
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
If the standard deviation of a data is 3.6 and each value of the data is divided by 3, then find the new variance and new standard deviation
The rainfall recorded in various places of five districts in a week are given below. Find its standard deviation
| Rainfall (in mm) | 45 | 50 | 55 | 60 | 65 | 70 |
| Number of places | 5 | 13 | 4 | 9 | 5 | 4 |
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 |
The range of the data 8, 8, 8, 8, 8 ........ 8 is
The sum of all deviations of the data from its mean is
The mean of the following frequency distribution is 62.8 and the sum of all frequencies is 50. Compute the missing frequencies f1 and f2.
| Class Interval | 0 − 20 | 20 − 40 | 40 − 60 | 60 − 80 | 80 − 100 | 100 − 120 |
| Frequency | 5 | f1 | 10 | f2 | 7 | 8 |
If the range and coefficient of range of the data are 20 and 0.2 respectively, then find the largest and smallest values of the data
