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 Variance of five observations$x = 1$,$x = 3$,$x = a$,$x = 7$and$x = b$,$a > b$, be 5 and 10 1 2 3 4 5 respectively. Then the Variance of the observations$n + x$,$n = 1$, 2,$\ldots$$\ldots$. .5 is n
The range of the following set of observations 2, 3, 5, 9, 8, 7, 6, 5, 7, 4, 3 is
For a data set having 100 observations, mean, median, mode are 50, 60, 70 respectively. If the largest 50 observations are increased by 10, then sum of new mean, median, mode equals
Consider the frequency distribution: Class: $0$-$10$, $10$-$20$, $20$-$30$, $30$-$40$, $40$-$50$, $50$-$60$; Frequency: $3$, $a$, $b$, $11$, $8$, $4$. If the mean is $\frac{277}{9}$ and median is $\frac{335}{11}$, then the value of $4a+b$ is
**Paragraph:** Let $X_1,X_2,\ldots,X_{18}$ be 18 observations such that $\displaystyle\sum_{i=1}^{18}(X_i-\alpha)=36$ and $\displaystyle\sum_{i=1}^{18}(X_i-\beta)^2=90$, where $\alpha$ and $\beta$ are distinct real numbers. If the standard deviation of these observations is 1, then the value of $|\alpha-\beta|$ is:
A) 2\quad B) 4\quad C) 5\quad D) 8
**Paragraph:** Let $X_1,X_2,\ldots,X_{18}$ be 18 observations such that $\displaystyle\sum_{i=1}^{18}(X_i-\alpha)=36$ and $\displaystyle\sum_{i=1}^{18}(X_i-\beta)^2=90$, where $\alpha$ and $\beta$ are distinct real numbers. If the standard deviation of these observations is 1, then the value of $|\alpha-\beta|$ is:
A) 2\quad B) 4\quad C) 5\quad D) 8
The mean and standard deviation of 10 observations $x_1, x_2, x_3, \ldots, x_{10}$ are $\bar{x}$ and $\sigma$ respectively. Let 10 is added to $x_1, x_2, \ldots, x_9$ and 90 is subtracted from $x_{10}$. If still, the standard deviation is the same, then $\bar{x}_{10} - \bar{x}$ is equal to
If the standard deviation of 0, 1, 2, $\ldots$, 9 is $k$, then the standard deviation of 10, 11, 12, $\ldots$, 19 is
Let the mean and variance of 8 numbers $-10,-7,-1,x,y,9,2,16$ be $\dfrac{7}{2}$ and $\dfrac{293}{4}$, respectively. Then the mean of 4 numbers $x,y,x+y+1,|x-y|$ is:
If $x_1, x_2, x_3, x_4, x_5, \ldots, x_n$ are $n$ observations such that $\sum_{i=1}^{n} x_i^2 = 400$ and $\sum_{i=1}^{n} x_i = 100$, then the possible value of $n$ among the following is
Let the mean and variance of 7 observations $2,4,10,x,12,14,y$, $x>y$, be 8 and 16 respectively. Two numbers are chosen from $\{1,2,3,x-4,y,5\}$ one after another without replacement, then the probability that the smaller number among the two chosen numbers is less than 4, is:
Frequency distribution with classes $[0,10),[10,20),\ldots,[50,60)$ and frequencies $3,c,d,11,5,5$ has mean $31$ and median $340/11$. Value of $\left[\tan^{-1}\!\dfrac{2cd}{d^2-c^2}\right]$ (GIF) is
For a data set having 100 observations, mean, median, mode are 50, 60, 70 respectively. If the largest 50 observations are increased by 10, then sum of new mean, median, mode equals
Frequency distribution with classes $[0,10),[10,20),\ldots,[50,60)$ and frequencies $3,c,d,11,5,5$ has mean $31$ and median $340/11$. Value of $\left[\tan^{-1}\!\dfrac{2cd}{d^2-c^2}\right]$ (GIF) is
Consider data on $X$ taking values $0, 2, 4, 8, \ldots, 2^n$ with frequencies ${}^nC_0, {}^nC_1, \ldots, {}^nC_n$ respectively. If the mean of this data is $\dfrac{728}{2^n}$, then $n$ is equal to
Let $\bar{x}$, $M$, $\sigma^2$ be mean, mode, variance of $n$ observations $x_1,\ldots,x_n$ and $d_i=-x_i-a$, $i=1,\ldots,n$. Statement 1: variance of $d_1,\ldots,d_n$ is $\sigma^2$. Statement 2: Mean and mode of $d_i$ are $-\bar{x}-a$ and $-M-a$ respectively.
Let \(a, b, c, d\) and \(e\) be the observations with mean \(m\) and standard deviation \(s\). The standard deviation of the observations \(a+k, b+k, c+k, d+k, e+k\) is