Question

which of the following is not an appropriate measure of center for a symmetric distribution?

inter quartile range
mean

Explanation:

Define measures of center

Using the Measures of Center knowledge point
Measures of center describe the middle or typical value of a data set. The most common measures of center are the mean, median, and mode. For a symmetric distribution, both the mean and the median are highly appropriate and typically equal or very close to each other.

Define interquartile range

Using the Interquartile Range knowledge point
The interquartile range (IQR) is calculated as \(Q_3 - Q_1\). It measures the spread or variability of the middle 50% of the data, rather than its central location. Therefore, it is a measure of spread (dispersion), not a measure of center.

Identify the correct option

Since the question asks which option is NOT an appropriate measure of center, we compare the choices:

• "Mean" is a measure of center.
• "Inter quartile range" is a measure of spread.

Thus, the interquartile range is the correct answer.

Answer:

• (A) Inter quartile range (Correct answer)
• (B) Mean