List of top Mathematics Questions on Variance and Standard Deviation asked in JEE Main

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

Let mean and variance of 6 observations a, b, 68, 44, 40, 60 be 55 and 194. If a > b then find a + 3b

Given data \(60, 60, 44, 58, 68, α, β, 56\) has mean \(58\), variance = \(66.2\), then find \(α^2 + β^2\).

Let the mean and variance of 12 observations be 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 m/n, where m and n are coprime, then m + n is equal to

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 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 first $50$ even natural numbers is