List of top Mathematics Questions on Variance and Standard Deviation

Let $X=\{x\in\mathbb{N}:1\le x\le19\}$ and for some $a,b\in\mathbb{R}$, $Y=\{ax+b:x\in X\}$. If the mean and variance of the elements of $Y$ are $30$ and $750$ respectively, then the sum of all possible values of $b$ is

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:

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

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 ________.

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

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

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 $ \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?

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

Find the variance of the data given below \[ \text{Size of item:} \quad 3.5, 4.5, 5.5, 6.5, 7.5, 8.5, 9.5 \\ \text{Frequency:} \quad 3, 7, 22, 60, 85, 32, 8 \]

If sample A contains 100 observations 101, 102, .... 200 and sample B contains 100 observations 151, 152, .... 250, then the ratio of variance $ \frac{V_A}{V_B} $ is:

Find the mean and variance for the first n natural numbers.

Find the mean and variance for the first 10 multiples of 3.

Find the mean and variance for the data

$x_i$	6	10	14	18	24	28	30
$f_i$	2	4	7	12	8	4	3

Find the mean and variance for the data

$x_i$	62	93	97	98	102	104	106
$f_i$	3	2	3	2	6	3	3

Find the mean and standard deviation using short-cut method.

$x_i$	60	61	62	63	64	65	66	67	68
$f_i$	2	1	12	29	25	12	10	4	5

Find the mean and variance for the following frequency distribution.

Classes	0-30	30-60	60-90	90-120	120-150	150-180	180-210
Frequencies	2	3	5	10	3	5	2

Find the mean and variance for the following frequency distribution.

Classes	0-10	10-20	20-30	30-40	40-50
Frequencies	5	8	15	16	6

Find the mean, variance and standard deviation using short-cut method.

Height in cms	70-75	75-80	80-85	85-90	90-95	95-100	100-105	105-110	110-115
No. of children	3	4	7	7	15	9	6	6	3

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

Diameters	No. of children
33-36	15
37-40	17
41-44	21
45-48	22
49-52	25

\(x_i\)	6	10	14	18	24	28	30
\(f_i\)	2	4	7	12	8	4	3

\(x_i\)	60	61	62	63	64	65	66	67	68
\(f_i\)	2	1	12	29	25	12	10	4	5