Advertisements
Advertisements
प्रश्न
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.
उत्तर
The remaining number of pages to be completed is 60 – 32, 60 – 35, 60 – 37, 60 – 30, 60 – 33, 60 – 36, 60 – 35 and 60 – 37
The pages to be completed are, 28, 25, 23, 30, 27, 24, 25, and 23
Arrange in ascending order we get, 23, 23, 24, 25, 25, 27, 28 and 30
| xi | xi2 |
| 23 | 529 |
| 23 | 529 |
| 24 | 576 |
| 25 | 625 |
| 25 | 625 |
| 27 | 729 |
| 28 | 784 |
| 30 | 900 |
| `sumx_"i"` = 205 | `sumx_"i"^2` = 5297 |
Here n = 8, `sumx_"i"` = 205, `sumx_"i"^2` = 5297
Standard deviation (σ) = `sqrt((sumx_"i"^2)/"n" - ((sumx_"i")/"n")^2`
= `sqrt(5297/8 - (205/8)^2`
= `sqrt(662.13 - 42025/64)`
= `sqrt(662.13 - 656.64)`
= `sqrt(5.49)`
= 2.34
Standard deviation (σ) = 2.34
APPEARS IN
संबंधित प्रश्न
Find the range and coefficient of range of the following data
63, 89, 98, 125, 79, 108, 117, 68
If the range and the smallest value of a set of data are 36.8 and 13.4 respectively, then find the largest value
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 |
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 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 |
Which of the following is not a measure of dispersion?
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 |
The diameter of circles (in mm) drawn in the design are given below.
| Diameters | 33 − 36 | 37 − 40 | 41 − 44 | 45 − 48 | 49 − 52 |
| Number of circles | 15 | 17 | 21 | 22 | 25 |
Calculate the standard deviation.
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.
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
