Which of the following statements is true about the distribution represented by a histogram that is symmetric and bell-shaped?

• A. The data is likely to be bimodal.
• B. The histogram represents a categorical variable.
• C. Most of the data values are found in the tails of the distribution.
• D. The $\mathrm{mean}$ and $\mathrm{median}$ of the data are approximately equal.

Answer: (D)

Verified step by step guidance

1. Understand the characteristics of a symmetric, bell-shaped distribution. Such a distribution is typically associated with the normal distribution, which is unimodal and continuous.
2. Recall that a symmetric distribution means the left and right sides of the histogram are mirror images, so the center measures (mean and median) are located at the same point.
3. Recognize that a bimodal distribution has two peaks, which contradicts the bell-shaped, unimodal nature described here.
4. Note that a histogram representing a categorical variable would show distinct bars for categories, not a smooth bell shape.
5. Understand that in a bell-shaped distribution, most data values cluster around the center, not in the tails, so the mean and median being approximately equal is the true statement.