Question

what type of data distribution is shown on the graph? negatively skewed

the mean is less than the median

the mode is
greater than the median
less than the median
equal to the median

Explanation:

Identify the distribution type

Using the Skewed Distribution Properties knowledge point, we observe that the tail of the probability distribution extends to the left (towards the lower values, \(X = 0\)), while the peak is on the right (\(X = 3\)). This shape is classified as negatively skewed (or left-skewed).

Compare the mean and median

Using the Mean vs Median in Skewed Data knowledge point, in a negatively skewed distribution, the extreme low values in the left tail pull the mean down more than they affect the median. Therefore, the mean is less than the median.

Compare the mode and median

In a unimodal, negatively skewed distribution, the peak of the graph represents the mode, which is located at the highest value on the right (\(X = 3\)). The median lies to the left of the mode, and the mean lies furthest to the left. Thus, the order of the measures of center from left to right is:

$$ \text{Mean} < \text{Median} < \text{Mode} $$

Consequently, the mode is greater than the median.

Answer:

What type of data distribution is shown on the graph? <blank>negatively skewed</blank>

The mean is <blank>less than the median</blank>

The mode is <blank>greater than the median</blank>