Let \(x_1, x_2, x_3, x_4, x_5\) be the observations with mean \(m\) and standard deviation \(s\). The standard deviation of the observations \(kx_1, kx_2, kx_3, kx_4, kx_5\) is
For the frequency distribution (class: 0-10, 10-20, 20-30, 30-40, 40-50; frequency: 2,3,x,5,4) with mean 28, the variance is ________.
The mean and the median of the following ten numbers in increasing order 10, 22, 26, 29, 34, x, 42, 67, 70, y are 42 and 35 respectively, then \(\frac{y}{x}\) is equal to
Mean and variance of 8 numbers $x,y,10,12,6,12,4,8$ are 9 and 9.25. If $x>y$, then $3x-2y$ is equal to _______
If both the mean and the standard deviation of 50 observations \(x_1, x_2, \ldots, x_{50}\) are equal to 16, then the mean of \((x_1 - 4)^2, (x_2 - 4)^2, \ldots, (x_{50} - 4)^2\) is ______.
If the mean and the variance of the data (Class 4–8, 8–12, 12–16, 16–20; Frequency 3, $\lambda$, 4, 7) are $\mu$ and 19 respectively, then the value of $\lambda+\mu$ is
Let $\alpha,\beta\in\mathbb{R}$. Let the mean and the variance of 6 observations $-3,4,7,-6,\alpha,\beta$ be 2 and 23, respectively. The mean deviation about the mean of these 6 observations is:
For 50 observations \(a, 2a, 3a, \ldots, 50a\), the mean deviation about the median is minimized and \(\dfrac{1}{n}\sum|x_i - A|\) is minimized when \(A\) is the median. If \(625a = 2500\), find \(a\).
Let $x_1, x_2, \ldots, x_{10}$ be ten observations such that $\displaystyle\sum_{i=1}^{10}(x_i - 2) = 30$, $\displaystyle\sum_{i=1}^{10}(x_i - \beta)^2 = 98$, $\beta > 2$, and their variance is $\frac{4}{5}$. If $\mu$ and $\sigma^2$ are respectively the mean and the variance of $2(x_1 - 1) + 4\beta, 2(x_2 - 1) + 4\beta, \ldots, 2(x_{10} - 1) + 4\beta$, then $\frac{\beta\mu}{\sigma^2}$ is equal to:
For a statistical data $x_{1},x_{2},\dots,x_{10}$ of $10$ values, a student obtained the mean as $5.5$ and $\sum_{i=1}^{10}x_{i}^{2}=371$. He later found that he had noted two values in the data incorrectly as $4$ and $5$, instead of the correct values $6$ and $8$, respectively. The variance of the corrected data is:
If the arithmetic mean of the numbers \(x_1, x_2, x_3, \ldots, x_n\) is \(\bar{x}\), then the arithmetic mean of the numbers \(ax_1 + b,\ ax_2 + b,\ ax_3 + b,\ \ldots,\ ax_n + b\), where \(a, b\) are two constants, would be
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
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
If a variable \(x\) takes values \(0, 1, 2, \ldots, n\) with frequencies proportional to the binomial coefficients \({}^nC_0, {}^nC_1, {}^nC_2, \ldots, {}^nC_n\), then \(\text{var}(X)\) is
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