Question

Select all of the true statements about the standard deviation of a quantitative variable. Standard deviation is resistive to unusual values. Standard deviation represents how far a group of values are from the mean of those values, on average. The standard deviation of a set of values is equal to 00 if and only if all of the values are the same. Changing the units of a set of values (e.g., converting from inches to feet) does not affect its standard deviation. Standard deviation is always a nonnegative value. If a set of values has a mean of 00 and a standard deviation that is not 0,0, then adding a new data point with a value of 00 will have no effect on the standard deviation.

Answer 1

Answer:

Step-by-step explanation:

The correct answers are:

1.The std deviation represents how far a group of values are from the mean of those values, on average.  This is true because variance is taken as average of sum of squares of each value from the mean and square root is std dev

2. The std deviation can be zero only if all the values are the same. EVen if one value differs slightly, the mean will be different from each entry for atleast one and hence variance so std deviation will be positive and not zero

3. Changing the units does not affect std deviation. True.  Because when we change units corresponding mean changes deviation also changes but final answer would be the same

4, Std dev is always non negative. True because positive square root of variance is considered as std dev

5.True because when 0 is added mean remains the same. Also sum of square of 0 from 0 will not add anything to variance so std dev is the same

Answer 2

The standard deviation is defined as the data set, probability distribution random variable or sample is square root of its variance.

The given (i) and (ii) statement are correct.

Given:

Standard deviation is restive to unusual values.

(i)

Write the formula for standard deviation.

$\sigma =\sqrt{\dfrac{(x_i-\overline{x})^2}{N}$

Where, $x_i$ is value from population, $\sigma$ is population standard deviation, $\overline {x}$ is mean.

The above expression shows that the self standard deviation tell how far  a group or values from their mean.

Thus, the option (i) is correct.

(ii)

The standard deviation formula include square of deviation from mean due to which it can only take positive value so, no negative.

Thus, the option (ii) is correct.

(iii)

Let the set contain -2,0,2 if mean is zero.

$\sigma =\sqrt{\dfrac{(4+4)}{3}$

$\sigma =\sqrt{\dfrac{8}{3}}$

If 0 is removed mean square remain same.

$S.D=\sqrt{\dfrac{(-2-0)^2+(2-0)^2}{2}$

$S.D=2$

Here the standard deviation changed.

Thus the given statement is incorrect.

(iv)

For the standard deviation to be zero, there should not be any deviation or difference between the values and their mean, this is only possible when all values are same.

Thus, the given statement is incorrect.  

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