Question

The sum of $10$ observations is $110$ and the sum of squares of observations is $2900$, their standard deviation is ______.

• A. $13$
• B. $8$
• C. $10$
• D. $9$

Answer 1

The correct option is A $13$

Standard deviation is the square root of the arithmetic mean of the squares of the deviations measured from the arithmetic mean of the data.

Standard deviation = { (sum of the squares of the observations/ number of observations ) – (sum of observations/ number of observations ) } ^½

= { (2800/10) –(110/10) } ^½

= { 280- 11}^1/2

= (169) ^½

= 13