Question

select the correct description of this skewed distribution curve.

a.) left-skewed: the mode lies to the left of the mean
b.) left-skewed: the mode lies to the right of the mean
c.) right-skewed: the mode lies to the right of the mean
d.) right-skewed: the mode lies to the left of the mean

Explanation:

Identify the direction of skewness

The given distribution curve has a long tail extending to the right side. In statistics, a distribution is classified by the direction of its long tail. Since the tail stretches toward the larger values on the right, this is a right-skewed (or positively skewed) distribution.

Determine the relative positions of the mode and mean

In a right-skewed distribution, the extreme values in the long right tail pull the mean upward (to the right). The mode represents the peak of the curve, which remains on the left. Therefore, the mode is less than the mean, meaning the mode lies to the left of the mean on a standard horizontal axis.

Match with the given options

We look for the option that correctly identifies the distribution as "Right-skewed" and states that "the mode lies to the left of the mean":

• Option a: Left-skewed (Incorrect)
• Option b: Left-skewed (Incorrect)
• Option c: Right-skewed: the mode lies to the right of the mean (Incorrect, the mean is pulled to the right of the mode, so the mode is to the left of the mean)
• Option d: Right-skewed: the mode lies to the left of the mean (Correct)

Answer:

• a.) Left-skewed: the mode lies to the left of the mean
• b.) Left-skewed: the mode lies to the right of the mean
• c.) Right-skewed: the mode lies to the right of the mean
• d.) Right-skewed: the mode lies to the left of the mean (Correct answer)