Measures of central tendency

Consider a data consisting of 10 observations $x_1,x_2,\dots,x_{10}$, whose mean is $5$ and variance is $7$. If the mean and the variance of the first $8$ observations $x_1,x_2,\dots,x_8$ are $4$ and $3.5$, respectively, and $x_9<x_{10}$, then the value of $3x_9+2x_{10}$ is ________.

If the mean of the data

Class	5-10	10-15	15-20	20-25	25-30	30-35
Frequency	2	$k$	28	54	$k+1$	5

is 21, then $k$ is one of the roots of the equation :

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 $2a$ is equal to:

The mean deviation about the mean for the data

$x_i$	5	7	9	10	12	15
$f_i$	8	6	2	2	2	6

is equal to:

A variable X takes values $0,0,2,6,12,20,\dots,n(n-1)$ with frequencies ${}^nC_0,{}^nC_1,{}^nC_2,{}^nC_3,{}^nC_4,{}^nC_5,\dots,{}^nC_n$, respectively. If the mean of this data is 60, then its median is :

Consider the following frequency distribution:

Value	4	5	8	9	6	12	11
Frequency	5	$f_1$	$f_2$	2	1	1	3

Suppose that the sum of the frequencies is 19 and the median of this frequency distribution is 6.

For the given frequency distribution, let $\alpha$ denote the mean deviation about the mean, $\beta$ denote the mean deviation about the median, and $\sigma^2$ denote the variance.

Match each entry in List-I to the correct entry in List-II and choose the correct option.

Consider the given data with frequency distribution

$x_i$	3	8	11	10	5	4
$f_i$	5	2	3	2	4	4

Match each entry in List-I to the correct entries in List-II.

The correct option is:

If the mean deviation about the mean of the numbers 1, 2, 3, …, $n$, where $n$ is odd, is $\dfrac{5(n+1)}n$, then $n$ is equal to ______.

The mean of the numbers $a,b,8,5,10$ is 6 and their variance is 6.8. If M is the mean deviation of the numbers about the mean, then 25 M is equal to :

The mean and standard deviation of 50 observations are 15 and 2 respectively. It was found that one incorrect observation was taken such that the sum of correct and incorrect observations is 70. If the correct mean is 16, then the correct variance is equal to :

The mean and variance of the data 4, 5, 6, 6, 7, 8, $x$, $y$, where $x<y$, are 6 and $\dfrac94$ respectively. Then $x^4+y^2$ is equal to

Let the mean and the variance of 5 observations $x_1,x_2,x_3,x_4,x_5$ be $\dfrac{24}5$ and $\dfrac{194}{25}$ respectively. If the mean and variance of the first 4 observation are $\dfrac72$ and $a$ respectively, then $(4a+x_5)$ is equal to :

If the mean deviation about median for the numbers 3, 5, 7, 2k, 12, 16, 21, 24, arranged in the ascending order, is 6 then the median is

Let $x_1,x_2,x_3,\ldots,x_{20}$ be in geometric progression with $x_1=3$ and the common ratio $\dfrac12$. A new data is constructed replacing each $x_i$ by $(x_i-i)^2$. If $\bar x$ is the mean of new data, then the greatest integer less than or equal to $\bar x$ is ______.

If the mean and median of the data

x	0 − 10	10 − 20	20 − 30	30 − 40	40 − 50
f	3	6	2	x	y	Σf = 20

are equal, then $xy^2$ is equal to

The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If now the mean age of the teachers in this school is 39 years, then the age (in years) of the newly appointed teacher is :

If the mean deviation of the numbers 1, 1 + d, ..., 1 + 100d from their mean is 255, then a value of d is :

The mean of 5 observations is 5 and their variance is 124. If three of the observations are 1, 2 and 6 ; then the mean deviation from the mean of the data is :

The mean of the data set comprising of 16 observations is 16. If one of the observation valued 16 is deleted and three new observations valued 3, 4 and 5 are added to the data, then the mean of the resultant data, is :

Let the sum of the first three terms of an A.P. be 39 and the sum of its last four terms be 178. If the first term of this A.P. is 10, then the median of the A.P. is :