The standard deviation, the range, and the interquartile range (IQR) summarize the variability of the data. a. Why is the standard deviation usually preferred over the ranges? b. Why is the IQR sometimes preferred to the standard deviation? c. What is an advantage of the standard deviation over the IQR?

Step-by-step explanation:

a) The standard deviation is usually preferred over the range because it is calculated from all of the data and will not be impacted as much as the range when they are outliers,and the standard deviation uses all of the data.

b)The IQR sometimes referred to the standard deviation when there is an outlier because the IQR is less sensitive to this features than standard deviation.

that is the IQR is not affected by an outlier,while the standard deviation is affected by an outlier.

c)The advantage of the standard deviation over the IQR is the standard deviation takes into account the values of all observation,while the IQR uses only some of the data.

Given:

The exponential function is:

To find:

The domain of the given exponential function.

Solution:

We know that the general form of an exponential function is:

Where, a is the initial value and b is growth/decay factor.

This function is defined for all real values of x, so the domain of these type of functions is the set of all real number.

We have,

Here, a is 1 and b is 5.3. This function is defined for all real values of x

Therefore, the domain of these type of functions is the set of all real number or it can be written as .