List of top Mathematics Questions on Variance and Standard Deviation

Given below are two statements:
Statement I: The Geometric mean of a set of n observations is the nth root of their product. 
Statement II: If X1, X2, X3 ... Xn are the given n observations, then their G.M. is given by \(\sqrt{(X_1) (X_2) (X_3)....(X_n)}\) In the light of the above statements,
Standard Error of the sampling distribution of a statistic is given by
The arithmetic mean and standard deviation of a series of 20 items were calculated by a student as 20 cm and 5 cm, respectively. But while calculating them an item 13 was misread as 30. The correct standard deviation is
The Mean deviation about the Mean for the following data 6,7,10,12,13,4,8,12.
The standard deviation for the following distribution:
Class30-4040-5050-6060-7070-8080-9090-100
Frequency371215832
The mean and variance of the data \(4, 5, 6, 6, 7, 8, x, y\), where \(x<y\), are \(6\) and \(\frac{9}{4}\), respectively. Then \(x^4+y^2\) is equal to
The standard deviation of the data $6, 7, 8, 9, 10$ is
The outcome of each of $30$ items was observed; $10$ items gave an outcome $\frac{1}{2} - d$ each, $10$ items gave outcome $\frac{1}{2}$ each and the remaining 10 items gave outcome $\frac{1}{2} + d$ each. If the variance of this outcome data is $\frac{4}{3}$ then |d| equals :
The variance of the following continuous frequency distribution is
The variance of first $20$ natural numbers is
The variance of first $50$ even natural numbers is
The standard deviation of $9, 16, 23, 30, 37, 44, 51$ is
Find the variance of the data given below
Occurance $(x_i)$ Frequency $(f_i)$ Freq $\ast (x_i)$ $(x_i-mean)$ $(x_i-mean)^2$ $f_i(x_i-mean)^2$
3.5 3 10.5 -3.59 12.887 38.661
4.5 7 31.5 -2.59 6.707 46.952
5.5 22 121 121 2.528 55.609
6.5 60 390 -0.59 0.348 20.876
7.5 85 637.5 0.41 0.168 14.298
8.5 32 272 1.41 1.988 63.632
9.5 8 76 2.41 5.809 46.47
Total 217 1538.5 - - 286.498
The variance of first n odd natural numbers is $\frac{n^{2}-1}{3}$ : The sum of first n odd natural number is $n^2$ and the sum of square of first n odd natural numbers is $\frac{n\left(4n^{2}-1\right)}{3}.$
: The variance of first $n$ even natural numbers is $\frac{n^{2}-1}{4}$ : The sum of first $n$ natural numbers is $\frac{n\left(n+1\right)}{2}$ and the sum of squares of first $n$ natural numbers is $\frac{n\left(n+1\right)\left(2n+1\right)}{6}$
The standard deviation for the scores $1, 2, 3, 4, 5, 6$ and $7$ is $2$. Then, the standard deviation of $12, 23, 34, 45, 56, 67$ and $78$ is
The variance of first n odd natural numbers is $\frac{n^2 - 1}{3}$. The sum of first n odd natural number is $n^2$ and the sum of square of first n odd natural numbers is $\frac{ n (4n^2 + 1)}{3}$ .
The mean of 5 numbers is 10, and their variance is 16. If one number is increased by 5, what is the new mean?
Standard deviation of the numbers 31, 32, 33, ... , 46, 47 is
Let a, b, c, d and 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 and e + k is

Find the mean and variance for the following frequency distribution.

Classes0-1010-2020-3030-4040-50
Frequencies5815166

The diameters of circles (in mm) drawn in a design are given below

DiametersNo. of children
33-3615
37-4017
41-4421
45-4822
49-5225
Standard deviation of first $n$ odd natural numbers is

The sum and sum of squares corresponding to length x (in cm) and weight y (in gm) of 50 plant products are given below:

\(\sum_{i=1}^{50}x_i=212,\sum_{i=1}^{50}x_i^2=902.8,\sum_{i=1}^{50}y_i=261,\sum_{i=1}^{50}y_{i=1}^2=1457.6\)

Which is more varying, the length or weight?

The following is the record of goals scored by team A in a football session:

No. of goals scored01234
No. of matches19753

For the team B, mean number of goals scored per match was 2 with a standard deviation 1.25 goals. Find which team may be considered more consistent?