Final answer:
The correct statement is 'c. Mean and median are measures of center for a random variable'. Standard deviation is not a measure of center but a measure of spread, and a histogram is a type of frequency distribution represented graphically.
Step-by-step explanation:
The correct statement among the given options is c.
Mean and median are measures of center for a random variable. The mean is the average of the data points, obtained by dividing the sum of all the observations by the number of observations.
The median is the middle value that separates the higher half from the lower half of the data set. When the data is symmetrically distributed, the mean and the median will be the same.
The statement a. Standard deviation is the mean distance of the observations from their median is incorrect because the standard deviation is a measure of the spread of the data values around the mean, not the median.
Statement b. Standard deviation is a measure of center for a random variable is also incorrect since the standard deviation is a measure of spread or variability, not a measure of center.
Finally, statement d. Histograms are different from frequency distributions is misleading because a histogram is a type of frequency distribution that is graphically represented; they are related but not the same thing.
Standard deviation can be particularly useful in symmetrical distributions but may not be as effective in representing skewed distributions, where it is more informative to consider measures like the quartiles or the range.
correct statement is 'c. Mean and median are measures of center for a random variable