Question

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.
select an answer
select an answer
mode <= median <= mean
mean <= median <= mode
mean = median = mode
que
5 pts 1 details

Explanation:

Step1: Recall the properties of skewed and symmetric distributions

• For a right - skewed distribution (tail on the right), the mean is pulled towards the tail. So, \(mode\leqslant median\leqslant mean\).
• For a left - skewed distribution (tail on the left), the mean is pulled towards the tail. So, \(mean\leqslant median\leqslant mode\).
• For a symmetric distribution, the mean, median, and mode are equal. So, \(mean = median=mode\).

Step2: Analyze each histogram

• First histogram: It is right - skewed. So the order is \(mode\leqslant median\leqslant mean\).
• Second histogram: It is left - skewed. So the order is \(mean\leqslant median\leqslant mode\).
• Third histogram: It is symmetric. So the order is \(mean = median = mode\).

Answer:

First histogram: \(mode\leqslant median\leqslant mean\); Second histogram: \(mean\leqslant median\leqslant mode\); Third histogram: \(mean = median = mode\)