If bar{x} is the mean of x_{1}, x_{2}, ldots, | vedclass

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(B) We know that if $\bar{x}$ is the mean of $x_{1}, x_{2}, \ldots, x_{n},$ then $\bar{x} = \frac{\sum_{i=1}^{n} x_{i}}{n},$ which implies $\sum_{i=1}

Vedclass · Accepted Answer

$\left(a+\frac{1}{a}\right) \frac{\bar{x}}{2}$

Vedclass · Answer

(B) We know that if $\bar{x}$ is the mean of $x_{1}, x_{2}, \ldots, x_{n},$ then $\bar{x} = \frac{\sum_{i=1}^{n} x_{i}}{n},$ which implies $\sum_{i=1}^{n} x_{i} = n \bar{x}.$The new set of observations consists of $2n$ terms: $a x_{1}, a x_{2}, \ldots, a x_{n}$ and $\frac{x_{1}}{a}, \frac{x_{2}}{a}, \ldots, \frac{x_{n}}{a}.$The mean of these $2n$ observations is given by:Mean $= \frac{(a x_{1} + a x_{2} + \ldots + a x_{n}) + (\frac{x_{1}}{a} + \frac{x_{2}}{a} + \ldots + \frac{x_{n}}{a})}{2n}$$= \frac{a(x_{1} + x_{2} + \ldots + x_{n}) + \frac{1}{a}(x_{1} + x_{2} + \ldots + x_{n})}{2n}$$= \frac{a(n \bar{x}) + \frac{1}{a}(n \bar{x})}{2n}$$= \frac{n \bar{x} (a + \frac{1}{a})}{2n}$$= \frac{\bar{x}}{2} (a + \frac{1}{a}).$

Mid-point	Frequency
$5$	$4$
$15$	$8$
$25$	$13$
$35$	$12$
$45$	$6$

Class interval	Frequency
$150-153$	$7$
$154-157$	$7$
$158-161$	$15$
$162-165$	$10$
$166-169$	$5$
$170-173$	$6$

Head	Expenditure (in $Rs$)
Food	$4000$
Education	$2500$
Clothing	$1000$
House Rent	$3500$
Others	$2500$
Savings	$1500$

If $\bar{x}$ is the mean of $x_{1}, x_{2}, \ldots, x_{n},$ then for $a \neq 0,$ the mean of $a x_{1}, a x_{2}, \ldots, a x_{n}, \frac{x_{1}}{a}, \frac{x_{2}}{a}, \ldots, \frac{x_{n}}{a}$ is

Similar Questions

Prepare a continuous grouped frequency distribution from the following data:

Mid-point Frequency

$5$ $4$

$15$ $8$

$25$ $13$

$35$ $12$

$45$ $6$

Also,find the size of the class intervals.

Convert the given frequency distribution into a continuous grouped frequency distribution:

Class interval Frequency

$150-153$ $7$

$154-157$ $7$

$158-161$ $15$

$162-165$ $10$

$166-169$ $5$

$170-173$ $6$

In which intervals would $153.5$ and $157.5$ be included?

When the investigator has personally obtained the information for a particular purpose,this data is called ........ data.

The expenditure of a family on different heads in a month is given below:

Head Expenditure (in $Rs$)

Food $4000$

Education $2500$

Clothing $1000$

House Rent $3500$

Others $2500$

Savings $1500$

Draw a bar graph to represent the data above.

State whether each of the following statements is true or false:
$(1)$ The median of the observations $12, 13, 14, 15, 16$ is $14$.
$(2)$ The mode of the observations $1, 3, 5, 7, 9$ is $5$.

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