Home
Class 12
MATHS
The variance of the series a,a+d,a+2d, …...

The variance of the series a,a+d,a+2d, …., a+2nd is :

A

a + (n - 1) d

B

a + nd

C

a + (n + 1) d

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
Required mean `(a+(a+d) +(a+2d)+ ...+(a+2nd))/(2n+1)`
`=((2n+1)/(2){2a+(2n+1-1)d})/(2n+1)=a+nd`
Promotional Banner

Topper's Solved these Questions

  • MEASURES OF CENTRAL TENDENCY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|40 Videos

  • MEASURES OF CENTRAL TENDENCY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|21 Videos

  • MEASURES OF CENTRAL TENDENCY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|21 Videos

  • MAXIMA AND MINIMA

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|29 Videos

  • MISCELLANEOUS EQUATIONS AND INEQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|29 Videos

Similar Questions

Explore conceptually related problems

The mean deviation of the series a , a+d , a+2d , , a+2n from its mean is ((n+1)d)/(2n+1) (b) (n d)/(2n+1) (c) (n(n+1)d)/(2n+1) (d) ((2n+1)d)/(n(n+1))

The mean deviation of the series a , a+d , a+2d ,.....,a+2n from its mean is (a) ((n+1)d)/(2n+1) (b) (n d)/(2n+1) (c) (n(n+1)d)/(2n+1) (d) ((2n+1)d)/(n(n+1))

The standard deviation of a, a+d, a + 2d,….a + 2nd is

Mean deviation of the series a^(2), a^(2)+d, a^(2)+2d, ………………., a^(2)+2nd from its mean is

If variance of variables a ,2a ,2a ,3a ,3a ,3a ,dot,10 a is 54 then value of ' a ' can be 3 (b) -3 (c) 9 (d) 6

Find the mean deviation from the mean of the A.P., a,a+d, a+2d, .........,a+2nd.

The sum of the series a-(a+d)+(a+2d)-(a+3d)+... up to (2n+1) terms is: a. -n d . b. a+2n d . c. a+n d . d. 2n d

The length of the diagonal of a square is d units. The area of the square is (a) d^2 (b) 1/2d^2 (c) 1/4d^2 (d) 2d^2

State the reason for the following : (i) Cu (I) ion is not stable in an aqueous solution. (ii) Unlike Cr^(3+),Mn^(2+),Fe^(3+) and the subsequent other M^(2+) ions of the 3d series, the 4d and 5d series metals generally do not form stable oxidation states.

Statement-1: The sum of n terms of the series a+(a+d)+(a+2d)+...(a+(n-1)d)=(n)/(2)[2a+(n-1)d] Statement-2:- Mathematical induction is valid only for natural numbers.

OBJECTIVE RD SHARMA ENGLISH-MEASURES OF CENTRAL TENDENCY-Section I - Solved Mcqs
  1. If the average of a, b, c and d is the average of b and c, then whic...

    Text Solution

    |

  2. If the arithmetic mean of the following data is 7, then a + b = {:(x...

    Text Solution

    |

  3. The average of n numbers x(1),x(2),x(3),..,x(n) is M. If x(n) is repla...

    Text Solution

    |

  4. For a symmetrical distribution Q(1) =20 and Q(3) =40. The value of 5...

    Text Solution

    |

  5. The variance of the series a,a+d,a+2d, …., a+2nd is :

    Text Solution

    |

  6. If the mean of the following data is 5.5, then x = {:(x(i),2,4,6,...

    Text Solution

    |

  7. The median of the data 5 , 6 , 7, 8 , 9 , 10 is "".

    Text Solution

    |

  8. The Median of the following discrete series is {:(x(i),3,6,5,8,12,...

    Text Solution

    |

  9. The median class in the following frequency distribution is {:("Cla...

    Text Solution

    |

  10. The number of observations in a group is 40. If the average of first 1...

    Text Solution

    |

  11. GM of the numbers 3,3^2,3^3,...,3^n is

    Text Solution

    |

  12. If the median of 25 observations is 45 and if the observations greater...

    Text Solution

    |

  13. The median of a set of nine distinct observations is 20.5. If each of ...

    Text Solution

    |

  14. A boy goes to a school from his home at a speed of x km/hr and comes b...

    Text Solution

    |

  15. A particle covers half of its total distance with speed v(1) and the r...

    Text Solution

    |

  16. A person purchases 1 kg of tomatoes from each of the 4 places at th...

    Text Solution

    |

  17. The mode of the following distribution is {:("Class interval :",1-5...

    Text Solution

    |

  18. The median of 100 observations grouped in classes of equal width is 25...

    Text Solution

    |

  19. The age distribution of 400 persons in a colony having median age 3...

    Text Solution

    |

  20. The mean of the data set comprising of 16 observations is 16. If one...

    Text Solution

    |