Home
Class 11
MATHS
Given that bar x is the mean and sigma^2...

Given that `bar x` is the mean and `sigma^2` is the variance of n observations `x_1`, `x_2`,....`x_n`. Prove that the mean and variance of the observations `ax_1, ax_2, ax_3`,......,`ax_n` are a `bar x` and `a^2 sigma^2`, respectively, `(a ne 0)`.

Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Given that bar x is the mean and sigma^2 is the variance of n observations x_1, x_2, ... x_n . Prove that the mean and variance of the observations ax_1, ax_2, ... ,ax_n , are a bar x and a^2 sigma^2 respectively (a ne 0) .

If barx represents the mean of n observations x_1, x_2,…….,x_n , then value of sum_(i=1)^n (x_1-barx) is :

The mean of n observations x_1,x_2,…………..x_n is barx . If (p+q) is added to each observations then prove that the mean of the new set of observations is barx+(p+q) .

If the mean of n observatoins: ax_1,ax_2,………..ax_n is abarx , Show that (ax_1-abarx)+(ax_2-abarx)+……..+(ax_n-abarx)=0

The mean and variance of a random variable X having a binomial distribution are 4 and 2 respectively, then P(X=1) is

If each of the observations x_1, x_2, ....x_n is increased by an amount ‘a’, where ‘a’ is a negative or positive number, show that the variance remains unchanged.

If the system of equations ax+y=1,x+2y=3,2x+3y=5 are consistent, then a is given by

If barx is the mean of x1,x2,x3, ………..xn , then for a ne 0, the mean of ax_1,ax_2,…..,ax_n,(x_2)/a, (x_2)/a ,……., (x_n)/a is :

PSEB-STATISTICS-EXERCISE
  1. Find the mean deviation about the mean for the data given below:- 4,7,...

    Text Solution

    |

  2. Find the mean deviation about the mean for the data given below:- 38,7...

    Text Solution

    |

  3. Find the mean deviation about the median for the data given below:- 13...

    Text Solution

    |

  4. Find the mean deviation about the median for the data given below:- 36...

    Text Solution

    |

  5. Find the mean deviation about the mean for the data given below:- . xi...

    Text Solution

    |

  6. Find the mean deviation about the mean for the data given below:- xi 1...

    Text Solution

    |

  7. Find the mean deviation about the median for the data given below:- xi...

    Text Solution

    |

  8. Find the mean deviation about the median for the data given below:-xi ...

    Text Solution

    |

  9. Find the mean and variance for the following data:- 6, 7, 10, 12, 13, ...

    Text Solution

    |

  10. Find the mean and variance for the following data:- First n natural nu...

    Text Solution

    |

  11. Find the mean and variance for the following data:- First 10 multiples...

    Text Solution

    |

  12. The sum and sum of squares corresponding to length x (in cm) and weigh...

    Text Solution

    |

  13. The mean and variance of eight observations are 9 and 9.25, respective...

    Text Solution

    |

  14. The mean and variance of 7 observations are 8 and 16, respectively. If...

    Text Solution

    |

  15. The mean and standard deviation of six observations are 8 and 4, respe...

    Text Solution

    |

  16. Given that bar x is the mean and sigma^2 is the variance of n observat...

    Text Solution

    |

  17. The mean and standard deviation of 20 observations are found to be 10 ...

    Text Solution

    |

  18. The mean and standard deviation of a group of 100 observations were fo...

    Text Solution

    |