Question

which of the following describes the probability distribution below? probability distribution bar graph with x-values 1,2,3,4,5 and y-axis (probability) from 0 to 0.8; bar heights: 1≈0.7, 2≈0.1, 3≈0.1, 4≈0.05, 5≈0
options:

• the mean is greater than the median, and the majority of the data points are to the left of the mean.
• the mean is greater than the median, and the majority of the data points are to the right of the mean.
• the median is greater than the mean, and the majority of the data points are to the left of the mean.
• the median is greater than the mean, and the majority of the data points are to the right of the mean.

Explanation:

Step1: Analyze the Distribution Shape

The probability distribution is right - skewed (long tail on the right). In a right - skewed distribution, the mean is pulled in the direction of the tail (to the right), so the mean is greater than the median.

Step2: Analyze Data Points Relative to Mean

In a right - skewed distribution, the majority of the data points (the bulk of the probability mass) are on the left - hand side (near the peak), and the mean is pulled to the right by the tail. So the majority of the data points are to the left of the mean.

Answer:

The mean is greater than the median, and the majority of the data points are to the left of the mean.