Statistics

A set of four observations has mean 1 and variance 13. Another set of six observations has mean 2 and variance 1 . Then, the variance of all these 10 observations is equal to :

A data consists of 20 observations $x_1, x_2, \ldots, x_{20}$. If $\sum\limits_{i=1}^{20}\left(x_i+5\right)^2=2500$ and $\sum\limits_{i=1}^{20}\left(x_i-5\right)^2=100$, then the ratio of mean to standard deviation of this data is :

Let the mean and the variance of seven observations $2,4, \alpha, 8, \beta, 12,14, \alpha<\beta$, be 8 and 16 respectively. Then the quadratic equation whose roots are $3 \alpha+2$ and $2 \beta+1$ is :

The mean deviation about the mean for the data
$$ \begin{array}{|c|c|c|c|c|c|c|} \hline x_i & 5 & 7 & 9 & 10 & 12 & 15 \\ \hline f_i & 8 & 6 & 2 & 2 & 2 & 6 \\ \hline \end{array} $$
\(\text { is equal to: }\)

A variable $X$ takes values $0,0,2,6,12,20, \ldots, n(n-1)$ with frequencies ${ }^n C_0,{ }^n C_1,{ }^n C_2,{ }^n C_3,{ }^n C_4,{ }^n C_5, \ldots,{ }^n C_n$, respectively. If the mean of this data is 60 , then its median is :

Suppose that the mean and median of the non-negative numbers $21,8,17, a, 51,103, b, 13,67,(a>b)$, are 40 and 21 , respectively. If the mean deviation about the median is 26 , then $2 a$ is equal to :

For 10 observations $x_1, x_2, \ldots, x_{10}$, if $\sum\limits_{i=1}^{10}\left(x_i+2\right)^2=180$ and $\sum\limits_{i=1}^{10}\left(x_i-1\right)^2=90$, then their standard deviation is :

If the mean of the datatable {width: 100%;border-collapse: collapse;margin: 20px 0;}th {background-color: blue;color: white;border: 1px solid lightgrey;padding: 10px;}td {border: 1px solid lightgrey;padding: 10px;text-align: left;}Class5-10...

The mean and variance of n observations are 8 and 16, respectively. If the sum of the first (n − 1) observations is 48 and the sum of squares of the first (n − 1) observations is 496, then the value of n is :

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

The mean and variance of a data of 10 observations are 10 and 2 , respectively. If an observations $\alpha$ in this data is replaced by $\beta$, then the mean and variance become 10.1 and 1.99 , respectively. Then $\alpha+\beta$ equals

Let $\mathrm{X}=\{x \in \mathrm{~N}: 1 \leq x \leq 19\}$ and for some $a, b \in \mathbb{R}, \mathrm{Y}=\{a x+b: x \in \mathrm{X}\}$. If the mean and variance of the elements of Y are 30 and 750 , respectively, then the sum of all possible v...

Let the mean and variance of 8 numbers $-10,-7,-1, x, y, 9,2,16$ be $\frac{7}{2}$ and $\frac{293}{4}$, respectively.
Then the mean of 4 numbers $x, y, x+y+1,|x-y|$ is :

If the mean and the variance of the data
$$ \begin{array}{|c|c|c|c|c|} \hline \text { Class } & 4-8 & 8-12 & 12-16 & 16-20 \\ \hline \text { Frequency } & 3 & \lambda & 4 & 7 \\ \hline \end{array} $$
are $\mu$ and 19 respectively, then the ...

If the mean deviation about the median of the numbers $\mathrm{k}, 2 \mathrm{k}, 3 \mathrm{k}, \ldots ., 1000 \mathrm{k}$ is 500 , then $\mathrm{k}^2$ is equal to :

A random variable X takes values 0, 1, 2, 3 with probabilities $\frac{2a+1}{30}$, $\frac{8a-1}{30}$, $\frac{4a+1}{30}$, $b$ respectively, where $a, b \in \mathbb{R}$. Let $\mu$ and $\sigma$ respectively be the mean and standard deviation of...

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 $1...

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 :

Let the Mean and Variance of five observations $x_1=1, x_2=3, x_3=a, x_4=7$ and $x_5=\mathrm{b}, a>\mathrm{b}$, be 5 and 10 respectively. Then the Variance of the observations $n+x_n, n=1,2, \ldots, 5$ is

If the mean and the variance of $6,4, a, 8, b, 12,10,13$ are 9 and 9.25 respectively, then $a+b+a b$ is equal to :

Let $x_1, x_2, ..., x_{10}$ be ten observations such that $\sum\limits_{i=1}^{10} (x_i - 2) = 30$, $\sum\limits_{i=1}^{10} (x_i - \beta)^2 = 98$, $\beta > 2$, and their variance is $\frac{4}{5}$. If $\mu$ and $\sigma^2$ are respectively the...

For a statistical data $\mathrm{x}_1, \mathrm{x}_2, \ldots, \mathrm{x}_{10}$ 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 , ...

Marks obtains by all the students of class 12 are presented in a freqency distribution with classes of equal width. Let the median of this grouped data be 14 with median class interval 12-18 and median class frequency 12. If the number of s...

The variance of the numbers $8,21,34,47, \ldots, 320$ is _______.

The frequency distribution of the age of students in a class of 40 students is given below.

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If the variance of the frequency distribution

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Let \(\mathrm{a}, \mathrm{b}, \mathrm{c} \in \mathbf{N}\) and \(\mathrm{a}< \mathrm{b}< \mathrm{c}\). 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 \(\frac{136}{5}\), r...

The mean and standard deviation of 20 observations are found to be 10 and 2 , respectively. On rechecking, it was found that an observation by mistake was taken 8 instead of 12. The correct standard deviation is

Let the mean and the standard deviation of the probability distribution

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Let \(\alpha, \beta \in \mathbf{R}\). 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 :

Let the mean and the variance of 6 observations \(a, b, 68,44,48,60\) be \(55\) and \(194\), respectively. If \(a>b\), then \(a+3 b\) is

Let M denote the median of the following frequency distribution

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The variance \(\sigma^2\) of the data

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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 _________.

If the mean and variance of five observations are \(\frac{24}{5}\) and \(\frac{194}{25}\) respectively and the mean of the first four observations is \(\frac{7}{2}\), then the variance of the first four observations in equal to

Let $\mathrm{a}_1, \mathrm{a}_2, \ldots \mathrm{a}_{10}$ be 10 observations such that $\sum\limits_{\mathrm{k}=1}^{10} \mathrm{a}_{\mathrm{k}}=50$ and $\sum\limits_{\forall \mathrm{k} < \mathrm{j}} \mathrm{a}_{\mathrm{k}} \cdot \mathrm{a}_{...

The mean and standard deviation of 15 observations were found to be 12 and 3 respectively. On rechecking it was found that an observation was read as 10 in place of 12 . If \(\mu\) and \(\sigma^2\) denote the mean and variance of the correc...

Let the median and the mean deviation about the median of 7 observation $170,125,230,190,210$, a, b be 170 and $\frac{205}{7}$ respectively. Then the mean deviation about the mean of these 7 observations is :

Consider 10 observations $x_1, x_2, \ldots, x_{10}$ such that $\sum\limits_{i=1}^{10}\left(x_i-\alpha\right)=2$ and $\sum\limits_{i=1}^{10}\left(x_i-\beta\right)^2=40$, where $\alpha, \beta$ are positive integers. Let the mean and the varia...

Let the mean and variance of 8 numbers \(x, y, 10,12,6,12,4,8\) be \(9\) and \(9.25\) respectively. If \(x > y\), then \(3 x-2 y\) is equal to _____________.

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 \(\frac{m}{n}\), wh...

The mean and variance of a set of 15 numbers are 12 and 14 respectively. The mean and variance of another set of 15 numbers are 14 and \(\sigma^{2}\) respectively. If the variance of all the 30 numbers in the two sets is 13 , then $$\sigma^...

If the mean and variance of the frequency distribution

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If the variance of the frequency distribution

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Let the mean and standard deviation of marks of class A of 100 students be respectively 40 and $\alpha(>$

0 ), and the mean and standard deviation of marks of class $B$ of $n$ students be respectively 55 and 30

$-\alpha$. If the mean and ...

The mean and variance of 7 observations are 8 and 16 respectively. If one observation 14 is omitted and a and b are respectively mean and variance of remaining 6 observation, then \(\mathrm{a+3 b-5}\) is equal to ___________.

Let $S$ be the set of all values of $a_1$ for which the mean deviation about the mean of 100 consecutive positive integers $a_1, a_2, a_3, \ldots ., a_{100}$ is 25 . Then $S$ is :

Three rotten apples are mixed accidently with seven good apples and four apples are drawn one by one without replacement. Let the random variable X denote the number of rotten apples. If \(\mu\) and \(\sigma^2\) represent mean and variance ...

Let \(X=\{11,12,13,....,40,41\}\) and \(Y=\{61,62,63,....,90,91\}\) be the two sets of observations. If \(\overline x\) and \(\overline y\) are their respective means and \(\sigma^2\) is the variance of all the observations in $$\mathrm{X...

The mean and variance of the marks obtained by the students in a test are 10 and 4 respectively. Later, the marks of one of the students is increased from 8 to 12. If the new mean of the marks is 10.2, then their new variance is equal to :