Question

3.1: measures of center. extreme values and measure of center
histogram shapes and the relative locations of measures of centers
determine the most likely ordering of the measures of center for each distribution shown below.
question help: written example message instructor post to forum
submit question

Explanation:

Step1: Recall measure - center concepts

Measures of center include mean, median, and mode. For a right - skewed distribution, the mode is the peak, the median is in the middle of the ordered data, and the mean is pulled towards the tail. For a left - skewed distribution, the opposite is true. For a symmetric distribution, mean = median = mode.

Step2: Analyze first histogram

The first histogram is right - skewed. In a right - skewed distribution, the mode is the highest point on the left, the median is in the middle, and the mean is pulled to the right by the long tail. So the order is Mode < Median < Mean.

Step3: Analyze second histogram

The second histogram is left - skewed. In a left - skewed distribution, the mode is the highest point on the right, the median is in the middle, and the mean is pulled to the left by the long tail. So the order is Mean < Median < Mode.

Step4: Analyze third histogram

The third histogram is approximately symmetric. In a symmetric distribution, the mean, median, and mode are approximately equal. So the order is Mean ≈ Median ≈ Mode.

Answer:

For the first histogram: Mode < Median < Mean
For the second histogram: Mean < Median < Mode
For the third histogram: Mean ≈ Median ≈ Mode