The statement 'The median of a distribution is approximately equal to the

mean of the distribution' can be made true by adding which of the
following:

a. For all distributions
b. only for symmetric, mound-shaped distributions
c. For skewed distributions
d. For symmetric distributions
e. None of these

I am stuck between b and d. I am for certain that when mean is equal to
median the distribution is symmetric. If I had to guess, I would choose b.

I would choose b. For any symmetric distribution, the mean will be at the axis of symmetry of the distribution, and so will the median. The distribution does not have to be "mound shaped".

You are correct that when the mean and median are equal, the distribution is symmetric. However, this does not necessarily mean that the median of any distribution is approximately equal to the mean. Therefore, the correct choice would be option e, "None of these."

To determine the correct answer choice, let's analyze the given statement: 'The median of a distribution is approximately equal to the mean of the distribution.'

To establish the truth of this statement, we need to find conditions that make it hold. Let's consider each answer choice:

a. For all distributions: This answer choice suggests that the statement is true for any type of distribution. However, this is not accurate since the mean and median can be significantly different in certain cases. Therefore, option a is not correct.

b. Only for symmetric, mound-shaped distributions: A symmetric distribution, such as a normal distribution, has properties where the mean and median are equal. Hence, when the distribution is symmetric and mound-shaped, option b accurately describes the statement as true.

c. For skewed distributions: Skewed distributions have asymmetric shapes, leading to differences between the mean and median. So, option c contradicts the statement and is not correct.

d. For symmetric distributions: As discussed earlier, symmetric distributions do satisfy the given statement. Therefore, option d is correct.

e. None of these: While options a, c, and e are not correct, option b (only for symmetric, mound-shaped distributions) seems valid. However, since option d (for symmetric distributions) includes option b, it is a more appropriate answer choice.

Based on this analysis, the correct answer is d. The given statement is true for symmetric distributions.