Variance And Standard Deviation

The standard deviation for the following distribution:

Class	30-40	40-50	50-60	60-70	70-80	80-90	90-100
Frequency	3	7	12	15	8	3	2

The Mean deviation about the Mean for the following data 6,7,10,12,13,4,8,12.

Let is the mean of the variate values X₁, X₂,..., X_N. If a constant value A is subtracted from each variate value, then the resulting new mean is

Standard Error of the sampling distribution of a statistic is given by

The arithmetic mean and standard deviation of a series of 20 items were calculated by a student as 20 cm and 5 cm, respectively. But while calculating them an item 13 was misread as 30. The correct standard deviation is

Given below are two statements:
Statement I: The Geometric mean of a set of n observations is the nth root of their product.
Statement II: If X₁, X₂, X₃ ... X_n are the given n observations, then their G.M. is given by In the light of the above statements,