Home
Class 11
MATHS
Consider the first 10 positve integers ....

Consider the first 10 positve integers .If we multiply each number by -1 and then add 1 to each number,the variance of the number so obtained

A

8.25

B

6.5

C

3.87

D

2.87

Text Solution

Verified by Experts

The correct Answer is:
A
Since the first 10 positive intergers are 1,2,3,4,5,6,7,8, 9, and 10 on multiplying by-1 we get
-1,-2,-3,-4,-5,-6,-7,-8,-9,-10
On adding 1 in each number ,we get
0 -1,-2,-3,-4,-5,-6,-7,-8,-9
`therefore " " Sigmax_(i)=0-1-2-3-4-5-6-7-8-9`
`=-(9xx10)/2`
= - 45
`Sigma x_(i)^(2)=0^(2)+(-1)^(2)+(-2)^(2)+...+(-9)^(2)`
`- (9xx10xx190)/(6)`
285
`therefore " " SD =sqrt((285)/10-((-45)/10)^(2))=sqrt(285/10-2025/100)`
`=sqrt((2850-2025)/100)=sqrt(8.25)`
Now variance `=(SD)^(2)=(sqrt(8.25)^(2)=8.25`
Promotional Banner

Topper's Solved these Questions

  • STATISTICS

    NCERT EXEMPLAR ENGLISH|Exercise FILLERS|7 Videos

  • STATISTICS

    NCERT EXEMPLAR ENGLISH|Exercise LONG ANSWER TYPE QUESTIONS|8 Videos

  • SETS

    NCERT EXEMPLAR ENGLISH|Exercise TRUE AND FALSE|6 Videos

  • STRAIGHT LINES

    NCERT EXEMPLAR ENGLISH|Exercise MATCHING THE COLUMN|3 Videos

Similar Questions

Explore conceptually related problems

Cosider the number 1,2,3,4,5,6,7,8,9 and 10.If 1 is added to each number the variance of the number so obtained is

Consider the numbers 1,2,3,4,5,6,7,8,9,10. If 1 is added to each number, the variance of the numbers so obtained is

The variance of first n natural number is:

Consider the numbers 1,2,3,4,5,6,7,8,9,10. If 1 is added to each number, the variance of the numbers so obtained is (a) 6.5 (b) 2.87 (c) 3.87 (d) 8.25

Consider the numbers 1,2,3,4,5,6,7,8,9,10. If 2 is added to each number then variance of the numbers so obtained is (i) 6.5 (ii) 2.87 (iii) 3.87 (iv) 8.25

The sum of three numbers is 6. If we multiply third number by 3 and add second number to it, we get 11. By adding first and third numbers, we get double of the second number. Represent it algebraically and find the numbers using matrix method.

The variance of first 20 - natural numbers is

If three numbers are in G.P., then the numbers obtained by adding the middle number to each of these numbers are in

Find the variance of first 50 even natural numbers.

Three numbers are in G.P. Their sum is 14. If we multiply the first and third numbers by 4 and 2nd number by 5, the new numbers form an A.P. Find the numbers.