#### The mean and the standard deviation (s.d.) of 10 observations are 20 and 2 respectively. Each of these 10 observations is multiplied by p and then reduced by q, where and If the new mean and new s.d. become half of their original values, then q is equal to :Option: 1Option: 2Option: 3Option: 4

Some Important Point Regarding Statistics -

Some Important Point Regarding Statistics

1. The sum of the deviation of an observation from their mean is equal to zero. i.e. .
2. The sum of the square of the deviation from the mean is minimum, i.e.
3. The mean is affected accordingly if the observations are given a mathematical treatment i.e. addition, subtraction multiplication by a constant term.
4. If set of n1 observations has mean  and set of n2 observations has mean , then their combined mean is  and the .
5. If set of  n1 observations has mean  and set of n2 observations has mean  then their combined variance is given by

where,

are the means and   are the standard deviations of two series.

-

Old Mean

Old Standard Deviation

If each observation is multiplied with p & then q is subtracted

New mean is the half of old mean

and new standard deviations is the half of old mean

Case 1

Using equation 1

we get

Case 1

Using equation 1

we get

Correct Option (1)