Let $a,b,c\in\mathbb{N}$ and $a<b<c$. Let the mean, the mean deviation about the mean and the variance of the 5 observations $9,25,a,b,c$ be 18, 4 and $\dfrac{136}{5}$, respectively. Then $2a+b-c$ is equal to _____
The mean and variance of 10 observations are 9 and 34.2, respectively. If 8 of these observations are 2, 3, 5, 10, 11, 13, 15, 21, then the mean deviation about the median of all the 10 observations is
Let the mean and the standard deviation of the observation 2, 3, 3, 4, 5, 7, a, b be 4 and$\sqrt{2}$respectively. Then the mean deviation about the mode of these observations is :
If the mean of the numbers \(27 + x,\ 31 + x,\ 89 + x,\ 107 + x,\ 156 + x\) is 82, then the mean of \(130 + x,\ 126 + x,\ 68 + x,\ 50 + x,\ 1 + x\) is
Let observations be \(a_1, a_2, \ldots, a_n, a_{n+1}, a_{n+2}, \ldots, a_{2n}\). If \((a_1+5), (a_2+5), \ldots, (a_n+5)\) and \((a_{n+1}-3), (a_{n+2}-3), \ldots, (a_{2n}-3)\) are the new observations, then the new mean \(\bar{x}'\) equals:
Following are the marks obtained by 9 students in a mathematics test: 50, 69, 20, 33, 53, 39, 40, 65, 59. The mean deviation from the median 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
Find the harmonic mean of \(\frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \ldots, \frac{n}{n+1}\) occurring with frequencies \(1, 2, 3, \ldots, n\), respectively.
For \((2n+1)\) observations \(x_1, -x_1, x_2, -x_2, \ldots, x_n, -x_n\) and \(0\), where all \(x\)'s are distinct, let SD and MD denote the standard deviation and median, respectively. Then which of the following is always true?
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
For the frequency distribution $x_i: 2,4,6,8,10,12,14,16$ and $f_i: 4,4,\alpha,15,8,\beta,4,5$ with mean 9 and variance 15.08, then $\alpha^2+\beta^2-\alpha\beta$ is _____.
If the mean and variance of the data $65,68,58,44,48,45,60,\alpha,\beta,60$ where $\alpha>\beta$ are 56 and 66.2 respectively, then $\alpha^2+\beta^2$ is equal to
Let $a_1,a_2,\ldots,a_{10}$ be 10 observations such that $\displaystyle\sum_{k=1}^{10}a_k=50$ and $\displaystyle\sum_{\forall k<j}a_k\cdot a_j=1100$. Then the standard deviation of $a_1,a_2,\ldots,a_{10}$ is equal to:
Let $x_{1},x_{2},\dots,x_{10}$ be ten observations such that $\sum_{i=1}^{10}(x_{i}-2)=30$, $\sum_{i=1}^{10}(x_{i}-\beta)^{2}=98,\ \beta>2$, and their variance is $\dfrac{4}{5}$. If $\mu$ and $\sigma^{2}$ are respectively the mean and the variance of $2(x_{1}-1)+4\beta,\ 2(x_{2}-1)+4\beta,\dots,2(x_{10}-1)+4\beta$, then $\dfrac{\beta\mu}{\sigma^{2}}$ is equal to:
For a statistical data $x_1, x_2, \ldots, x_{10}$ 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