Commerce (English Medium) कक्षा ११ - CBSE Question Bank Solutions

If for distribution `sum(x - 5)` = 3, `sum(x - 5)^2` = 43 and total number of items is 18. Find the mean and standard deviation.

Mean and standard deviation of 100 observations were found to be 40 and 10, respectively. If at the time of calculation two observations were wrongly taken as 30 and 70 in place of 3 and 27 respectively, find the correct standard deviation.

The standard deviation of the data 6, 5, 9, 13, 12, 8, 10 is ______.

Let x₁, x₂, ..., x_n be n observations and `barx` be their arithmetic mean. The formula for the standard deviation is given by ______.

Let a, b, c, d, e be the observations with mean m and standard deviation s. The standard deviation of the observations a + k, b + k, c + k, d + k, e + k is ______.

Let x₁, x₂, x₃, x₄, x₅ be the observations with mean m and standard deviation s. The standard deviation of the observations kx₁, kx₂, kx₃, kx₄, kx₅ is ______.

Let x₁, x₂, ... xn be n observations. Let wi = lx_i + k for i = 1, 2, ...n, where l and k are constants. If the mean of x_i’s is 48 and their standard deviation is 12, the mean of w_i’s is 55 and standard deviation of w_i’s is 15, the values of l and k should be ______.

Standard deviations for first 10 natural numbers is ______.

Coefficient of variation of two distributions are 50 and 60, and their arithmetic means are 30 and 25 respectively. Difference of their standard deviation is ______.

If the variance of a data is 121, then the standard deviation of the data is ______.

The standard deviation of a data is ______ of any change in orgin, but is ______ on the change of scale.

The standard deviation is ______to the mean deviation taken from the arithmetic mean.

The mean and standard deviation of six observations are 8 and 4, respectively. If each observation is multiplied by 3, find the new mean and new standard deviation of the resulting observations.

Evaluate the following limit.

`lim_(x -> pi) (sin(pi - x))/(pi (pi - x))`

Evaluate the following limit.

`lim_(x ->0) cos x/(pi - x)`

Evaluate the following limit.

`lim_(x -> 0) (cos 2x -1)/(cos x - 1)`

Evaluate the following limit.

`lim_(x -> 0) (ax +  xcos x)/(b sin x)`

Evaluate the following limit.

`lim_(x → 0) x sec x`

Evaluate the following limit.

`lim_(x -> 0) (sin ax + bx)/(ax + sin bx) a, b, a+ b != 0`

Evaluate the following limit.

`lim_(x -> 0) (cosec x -  cot x)`