Question

the mean and standard deviation of a set of observations are 10 and 16 respectively if all observations are halved what will be the new mean and standard deviation
a)10,16
b) 5,16
c)5,8
d)10,8

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Answer 1

Answer:

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Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

The mean and standard deviation of a set of observations are 10 and 16 respectively if all observations are halved what will be the new mean and standard deviation

a) 10 , 16

b) 5 , 16

c) 5 , 8

d) 10 , 8

CONCEPT TO BE IMPLEMENTED

For a given set of observations if each term of the observations multiplied by d then

New Mean = d × Old Mean

New Variance = d² × Old Variance

New standard deviation = d × Old Standard deviation

EVALUATION

Here it is given that the mean and standard deviation of a set of observations are 10 and 16 respectively

Now all observations are halved

So

$\displaystyle \sf{New \: mean = \frac{1}{2} \times Old \: mean }$

$\displaystyle \sf{ \implies \: New \: mean = \frac{1}{2} \times 10 }$

$\displaystyle \sf{ \implies \: New \: mean = 5 }$

Now

$\displaystyle \sf{\: New \: standard \: deviation = \frac{1}{2} \times old \: standard \: deviation }$

$\displaystyle \sf{ \implies \: New \: standard \: deviation = \frac{1}{2} \times 16}$

$\displaystyle \sf{ \implies \: New \: standard \: deviation = 8}$

FINAL ANSWER

Hence the correct option is c) 5 , 8

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