Question

in a normal distribution curve, the center of the curve represents the ______.

a.) mode only
b.) mean, median, and mode
c.) mean and mode only
d.) mean only

Explanation:

Analyze properties of a normal distribution

A normal distribution is a perfectly symmetric, bell-shaped probability distribution.

Identify the measures of center at the peak

Because of its perfect symmetry:

• The peak of the curve represents the most frequent value, which is the mode.
• The line of symmetry divides the area under the curve into two equal halves, meaning exactly \(50\%\) of the values lie below it and \(50\%\) lie above it, which is the median.
• The arithmetic average of the symmetric distribution lies exactly at the center of symmetry, which is the mean.

Therefore, at the center of a normal distribution curve, the mean, median, and mode are all equal and located at the same central point.

Answer:

• a.) mode only
• b.) mean, median, and mode (Correct answer)
• c.) mean and mode only
• d.) mean only