List of top Mathematics Questions on Variance and Standard Deviation

The mean and standard deviation of 100 observations are 40 and 5.1, respectively. By mistake one observation is taken as 50 instead of 40. If the correct mean and the correct standard deviation are $ \mu $ and $ \sigma $ respectively, then $ 10(\mu + \sigma) $ is equal to:

If the mean and the variance of 6, 4, a, 8, b, 12, 10, 13 are 9 and 9.25 respectively, then \(a + b + ab\) is equal to:

Let the mean and the standard deviation of the observations $ 2, 3, 4, 5, 7, a, b $ be $ 4 $ and $ \sqrt{2} $ respectively. Then the mean deviation about the mode of these observations is:
Variance of 240, 260, 270, 280
Find the standard deviation of the numbers: -3, 0, 3, 8.
From a lot of 12 items containing 3 defectives, a sample of 5 items is drawn at random. Let the random variable $X$ denote the number of defective items in the sample. Let items in the sample be drawn one by one without replacement. If the variance of $X$ is $\frac{m}{n}$, where $\gcd(m, n) = 1$, then $n - m$ is equal to ________.
If the mean deviation about the mean is \(m\) and the variance is \(\sigma^2\) for the following data, then \(m + \sigma^2 =\) % Data table \[ \begin{array}{|c|c|c|c|c|c|} \hline x & 1 & 3 & 5 & 7 & 9 \\ \hline f & 4 & 24 & 28 & 16 & 8 \\ \hline \end{array} \]
The standard deviation of 25 numbers is $ \sigma $. If each of the numbers is increased by 5, then the new standard deviation will be
Let $f : \mathbb{R} \to \mathbb{R}$ be given by $f(x) = \tan x$. Then $f^{-1}(1)$ is:
Let $a$, $b$, $c$, and $d$ be the observations with mean $m$ and standard deviation $S$. The standard deviation of the observations $a + k, b + k, c + k, d + k$ is:
7 coins are tossed simultaneously and the number of heads turned up is denoted by the random variable \( X \). If \( \mu \) is the mean and \( \sigma^2 \) is the variance of \( X \), then \( \frac{\mu^2}{P(X = 3)} \) is:
Let mean and variance of 6 observations a, b, 68, 44, 40, 60 be 55 and 194. If a > b then find a + 3b
The mean of 5 observations is \(\frac {24}{5}\) and variance is \(\frac {194}{25}\) . If the mean of first four observations is \(\frac 72\) , then the variance of first four observations is
The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. On respectively, it was found that an observation by mistake was taken 8 instead of 12. The correct standard deviation is
Given data \(60, 60, 44, 58, 68, α, β, 56\) has mean \(58\), variance = \(66.2\), then find \(α^2 + β^2\).
The variance of 20 observations is 5. If each one of the observations is multiplied by 2, then the variance of the resulting observations is:
The coefficient of variation of the two frequency distributions is 60% and 40% respectively. Both series have the same mean = 15. What is their standard deviation?
Let, the coefficient of variation of two datasets be \(50 \) and \(75\) ,respectively and the corresponding variances be \(25\) and \(36\),respectively.Also let \(x_1\) and \(x_2\) denote the corresponding sample means. Then \(x_1+x_2\) is ?

For four observations X,X2,X3,X4, it is given that ,\(∑x_i^{2}=656\) and  \(∑x_i=32\). Then, the variance of these four observations is ?

Let \(x\) denote the mean of the observations \(1,3,5,a,9\) and \(y\) denote the mean of the observations \(2,4,b,6,8\) where \(a,b>0\) .If \(x=y\) ,the value of \(2(a-b)\) is ?
If the median of the observations \(4,6,7,x,x+2,12,12,13\) arranged in an increasing order is 9,then the variance of these observations is 
Let the Standard deviation of \(x_1,x_2\) and \(x_3\) be \(9\) .Then ,the variance of \(3x_1+4,\)  \(3x_2+4 \) and \(3x_3+4\) is 

Let the mean and variance of 12 observations be \( \frac{9}{2} \) and 4, respectively. Later on, it was observed that two observations were considered as 9 and 10 instead of 7 and 14 respectively. If the correct variance is \( \frac{m}{n} \), where \( m \) and \( n \) are coprime, then \( m + n \) is equal to:

For two groups of 15 sizes each, mean and variance of first group is 12, 14 respectively, and second group has mean 14 and variance of σ2. If combined variance is 13 then find variance of second group?

Let is the mean of the variate values X1, X2,..., XN. If a constant value A is subtracted from each variate value, then the resulting new mean is