Statistics Test...

The mean is_____________________.

Consider the following statements:
(1) Mean is independent of change in scale and change in origin
(2) Variance is independent of change in scale but not in origin
Which of the above statements is/are correct?

The arithmetic mean between $$\cfrac { x+a }{ x } $$ and $$\cfrac { x-a }{ x } $$ when $$x\ne 0$$, is (the symbol $$\ne$$ means "not equal to"):

Consider the following statements:
$$1.$$ Variance is unaffected by change of origin and change of scale.
$$2.$$ Coefficient of variance is independent of the unit of observations.
Which of the statements given above is/ are correct?

The average (arithmetic mean) of a set of seven numbers is $$8$$. When an eighth number is added to the set, the average of the eight numbers is still $$8$$. What number was added to the set?

Consider the following statements:
$$1.$$ Coefficient of variation depends on the unit of measurement of the variable.
$$2.$$ Range is a measure of dispersion.
$$3.$$ Mean deviation is least when measured about median.
Which of the above statements are correct?

If the mode of five observations, in order, $$0, 2, 3, m, 5$$ is $$3$$ then $$m =$$ _______.

Find out the coefficient of range for the following prices of shirts in a shop.

Find out the range for the following prices of shirts in a shop.

Let mean of $$100$$ data points be $$55$$ and variance be $$16$$ . Now if every data point is increased by $$2$$ units, then the sum of mean and standard deviation of new data point will be: