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 : Option 1) 16.8 Option 2) 16.0 Option 3) 15.8 Option 4) 14.0

As we learnt in

ARITHMETIC Mean -

For the values x1, x2, ....xn of the variant x the arithmetic mean is given by

$\dpi{100} \bar{x}= \frac{x_{1}+x_{2}+x_{3}+\cdots +x_{n}}{n}$

in case of discrete data.

-

$\frac{\sum xi}{16}= 16$

$\Rightarrow \sum_{i=1}^{18}v_{i}= \left ( 16\times 16-16 \right )+\left ( 3+4+5 \right )=252$

number of observations=18

$mean=\frac{252}{18}= 14$

Option 1)

16.8

This option is incorrect

Option 2)

16.0

This option is incorrect

Option 3)

15.8

This option is incorrect

Option 4)

14.0

This option is correct

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