Which of the following statements can be inferred about the Mean, Median, and…
2025
Which of the following statements can be inferred about the Mean, Median, and Mode of the normal distribution P(x) for a variable x ?
- A.
MEAN ≠ MEDIAN = MODE
- B.
MEAN = MEDIAN = MODE
- C.
MEAN = MEDIAN ≠ MODE
- D.
MEAN ≠ MODE = MEDIAN
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Correct answer: B
Step-by-Step Solution
To determine the relationship between the mean, median, and mode for a normal distribution, we look at the shape of the curve:
Symmetry: A normal distribution is perfectly symmetric about its center.
Mean (Average): Because the distribution is perfectly balanced, the arithmetic average (mean) is located exactly at the center of the distribution.
Median (Middle Value): Since the distribution is symmetric, exactly 50% of the data lies to the left of the center and 50% lies to the right, meaning the median also falls exactly at the center.
Mode (Most Frequent Value): The peak of the normal distribution curve represents the highest probability density, which is at the center. Thus, the mode also coincides with the center.
Because all three measures—the mean, the median, and the mode—are located at the same central point, they are equal: MEAN = MEDIAN = MODE.