The mean of 10 observations is 48. If each ob | vedclass

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(C) Let the $10$ observations be $x_1, x_2, ..., x_{10}$.The mean of these observations is given by $\bar{x} = \frac{\sum_{i=1}^{10} x_i}{10} = 48$.Th

Vedclass · Accepted Answer

$16$

Vedclass · Answer

(C) Let the $10$ observations be $x_1, x_2, ..., x_{10}$.The mean of these observations is given by $\bar{x} = \frac{\sum_{i=1}^{10} x_i}{10} = 48$.Therefore,the sum of the observations is $\sum_{i=1}^{10} x_i = 48 	imes 10 = 480$.If each observation is divided by $3$,the new observations are $\frac{x_1}{3}, \frac{x_2}{3}, ..., \frac{x_{10}}{3}$.The new mean $\bar{x}'$ is given by $\bar{x}' = \frac{\sum_{i=1}^{10} (x_i / 3)}{10}$.$\bar{x}' = \frac{1}{3} 	imes \left( \frac{\sum_{i=1}^{10} x_i}{10} ight)$.Substituting the value of the original mean,we get $\bar{x}' = \frac{1}{3} 	imes 48 = 16$.Thus,the new mean is $16$.

Marks $(x_{i})$	$15$	$22$	$28$	$31$	$35$	$40$	$44$	$46$
Number of students $(f_{i})$	$2$	$3$	$5$	$6$	$6$	$4$	$3$	$1$

Marks	Number of students
$10-20$	$6$
$20-30$	$17$
$30-50$	$15$
$50-70$	$16$
$70-100$	$26$

The mean of $10$ observations is $48$. If each observation is divided by $3$,what will be the new mean?

Similar Questions

The information regarding the marks scored by $30$ students in a $50$ marks test is given below:

Marks $(x_{i})$ $15$ $22$ $28$ $31$ $35$ $40$ $44$ $46$

Number of students $(f_{i})$ $2$ $3$ $5$ $6$ $6$ $4$ $3$ $1$

Find the mean of the data.

$A$ class consists of $50$ students out of which $30$ are girls. The mean of marks scored by girls in a test is $73$ (out of $100$) and that of boys is $71$. Determine the mean score of the whole class.

The mean of $100$ observations is $50$. If one of the observations which was $50$ is replaced by $150$,the resulting mean will be:

If $\bar{x}$ represents the mean of $n$ observations $x_{1}, x_{2}, \ldots, x_{n},$ then the value of $\sum_{i=1}^{n}(x_{i}-\bar{x})$ is

The marks obtained (out of $100$) by a class of $80$ students are given below:
Marks Number of students
$10-20$ $6$
$20-30$ $17$
$30-50$ $15$
$50-70$ $16$
$70-100$ $26$

Construct a histogram to represent the data above.

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