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
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