Question

for the distribution shown below, identify the mean, median, and mode.

a. a = mode, b = median, c = mean
b. a = mode, b = mean, c = median
c. a = median, b = mode, c = mean
d. a = mean, b = mode, c = median

Explanation:

⚡ Using what you learned: comparing measures of center & spread

Step 1: Identify the shape of the distribution

The given curve has a long tail stretching to the left. This means the distribution is skewed to the left (negatively skewed).

Step 2: Determine the positions of the measures of center

In a skewed distribution, the three measures of center (mean, median, and mode) are pulled apart in a predictable order:

• Mode (A): The mode is the value where the curve reaches its highest peak. Looking at the graph, line \( A \) is directly under the peak of the distribution.

$$ \text{Mode} = A $$

• Mean (C): The mean is highly sensitive to extreme values. The long tail on the left pulls the mean furthest to the left, away from the peak.

$$ \text{Mean} = C $$

• Median (B): The median represents the middle value (50th percentile) and always lies between the mode and the mean in a skewed distribution.

$$ \text{Median} = B $$

Thus, we have:

• \( A = \text{mode} \)
• \( B = \text{median} \)
• \( C = \text{mean} \)

Answer:

A. A = mode, B = median, C = mean