(A) Given that the mean of $16$ observations is $16$,the sum of the observations is: $\sum_{i=1}^{16} x_i = 16 \times 16 = 256$. After deleting the ob

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(A) Given that the mean of $16$ observations is $16$,the sum of the observations is: $\sum_{i=1}^{16} x_i = 16 \times 16 = 256$. After deleting the observation with value $16$ and adding three new observations $(3, 4, 5)$,the new sum of the observations is: $\text{New Sum} = 256 - 16 + 3 + 4 + 5 = 252$. The new number of observations is $16 - 1 + 3 = 18$. The new mean is: $\text{New Mean} = \frac{252}{18} = 14$.

Class 11 Mathematics Statistics Word problem -Statistics

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

JEE MAIN 2015 All JEE MAIN

A
$14$
B
$16.8$
C
$16$
D
$15.8$

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The weighted mean of the first $n$ natural numbers,where the weights are equal to the squares of the corresponding numbers,is:

Difficult

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Consider the following statements:
$(1)$ Mode can be computed from a histogram.
$(2)$ Median is not independent of change of scale.
$(3)$ Variance is independent of change of origin and scale.
Which of these is/are correct?

MediumAIEEE 2004

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An analysis of monthly wages paid to the workers of two jute mills $A$ and $B$ gives the following data:

Metric Mill-$A$ Mill-$B$

No. of workers $500$ $600$

Average daily wage (in rupees) $186$ $175$

Variance of distribution of wages $81$ $100$

Then:

Metric	Mill-$A$	Mill-$B$
No. of workers	$500$	$600$
Average daily wage (in rupees)	$186$	$175$
Variance of distribution of wages	$81$	$100$

EasyAP EAMCET 2023

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The mean and variance of the marks obtained by $n$ 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:

DifficultJEE MAIN 2023

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The mean of $5$ observations is $4.4$ and their variance is $8.24$. If three of those observations are $1, 2$ and $6$,then the other two observations are:

DifficultAP EAMCET 2023

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

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The weighted mean of the first $n$ natural numbers,where the weights are equal to the squares of the corresponding numbers,is:

Consider the following statements:$(1)$ Mode can be computed from a histogram.$(2)$ Median is not independent of change of scale.$(3)$ Variance is independent of change of origin and scale.Which of these is/are correct?

An analysis of monthly wages paid to the workers of two jute mills $A$ and $B$ gives the following data: Metric Mill-$A$ Mill-$B$ No. of workers $500$ $600$ Average daily wage (in rupees) $186$ $175$ Variance of distribution of wages $81$ $100$ Then:

The mean and variance of the marks obtained by $n$ 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:

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Consider the following statements:
$(1)$ Mode can be computed from a histogram.
$(2)$ Median is not independent of change of scale.
$(3)$ Variance is independent of change of origin and scale.
Which of these is/are correct?

An analysis of monthly wages paid to the workers of two jute mills $A$ and $B$ gives the following data:

Metric Mill-$A$ Mill-$B$

No. of workers $500$ $600$

Average daily wage (in rupees) $186$ $175$

Variance of distribution of wages $81$ $100$

Then: