# Consider the following statements :(1) Mode can be computed from histogram(2) Median is not independent of change of scale(3) Variance is independent of change of origin and scale.Which of these is/are correct? Option 1) only (1) and (2) Option 2) only (2) Option 3) only (1) Option 4) (1), (2) and (3).

As we learnt in

MEDIAN -

The median is the middle of a distribution. Half the scores are above the median and half are below the median.

-

MODE -

The mode or modal value of a distribution is that value of the variable for which the frequency is maximum.

In case of a grouped or continuous frequency distribution mode is given by the formula.

$\dpi{80} Mode= l+\left ( \frac{f_{1}-f_{2}}{2f-f_{1}-f_{2}} \right )h$

- wherein

where

l is lower limit of the modal class.

h is width of the modal class.

f1 is frequency of the class preceding the modal class.

f2 is frequency of the class following the modal class.

f is frequency of the modal class.

Variance -

In case of discrete data

$\dpi{100} \sigma ^{2}= \left ( \frac{\sum x_{i}^{2}}{n} \right )-\left ( \frac{\sum x_{i}}{n} \right )^{2}$

-

(1) Mode can be computed by histogram because histogram can tell as about the highest frequency.

(2) Median depends on change of scale, as if the magnitude of observations change, median change as well.

(3) Variance depends on change of scale but is independent if we add, subtruct same number from all observation.

So (1) and (2) are correct

Option 1)

only (1) and (2)

Correct

Option 2)

only (2)

Incorrect

Option 3)

only (1)

Incorrect

Option 4)

(1), (2) and (3).

Incorrect

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