Question

select the correct description of this distribution curve.

left-skewed: mean < mode
right-skewed: mean > mode
left-skewed: mean > mode
right-skewed: mean < mode

Explanation:

Identify the direction of skewness

Using the Skewness Direction and Skewed Distributions knowledge points
The given distribution curve has a long tail extending to the left side, while the bulk of the data is concentrated on the right. A distribution with a longer or fatter tail on the left side is classified as left-skewed (also known as negatively skewed).

Compare the mean and the mode

Using the Measures of Center in Skew knowledge point
In a left-skewed distribution, the extreme low values in the left tail pull the mean down (to the left) more than they affect the median or the mode. The mode represents the peak of the curve, which remains on the right. Therefore, the mean is less than the mode:

$$ \text{mean} < \text{mode} $$

Answer:

• Left-skewed: mean < mode (Correct answer)
• Right-skewed: mean > mode
• Left-skewed: mean > mode
• Right-skewed: mean < mode