State with reason whether the following statements are True or False:
(i) Sum of square of the deviations of items from their arithmetic mean is the maximum.
(ii) Standard Deviation is based on all values.
(iii) For a given set of observations, standard deviation is always more than mean deviation from mean.
State with reason whether the following statements are True or False:
(i) Sum of square of the deviations of items from their arithmetic mean is the maximum.
(ii) Standard Deviation is based on all values.
(iii) For a given set of observations, standard deviation is always more than mean deviation from mean.
(i) False. The sum of square of the deviations of items from their arithmetic mean is the minimum. The sum is less than the sum of the square of the deviations of the items from any other value.
(ii) True. Standard deviation considers every item of the series. So, a change in even one value affects the value of standard deviation.
(iii) True. For a given set of observations, standard deviation is never less than mean deviation from mean, i.e., Standard Deviation > Mean Deviation from mean.
(i) False. The sum of square of the deviations of items from their arithmetic mean is the minimum. The sum is less than the sum of the square of the deviations of the items from any other value.
(ii) True. Standard deviation considers every item of the series. So, a change in even one value affects the value of standard deviation.
(iii) True. For a given set of observations, standard deviation is never less than mean deviation from mean, i.e., Standard Deviation > Mean Deviation from mean.
