Which of the following histograms is most likely to be approximately symmetric?

• A. A histogram with two distinct peaks at opposite ends
• B. A histogram with a single peak in the center and similar frequencies on both sides
• C. A histogram with a long tail to the right and most data concentrated on the left
• D. A histogram with a long tail to the left and most data concentrated on the right

Answer: (B)

Verified step by step guidance

1. Understand what it means for a histogram to be approximately symmetric: it should have a shape where the left and right sides are roughly mirror images of each other around a central peak.
2. Look at the option describing a histogram with two distinct peaks at opposite ends. This suggests a bimodal distribution, which is not symmetric because the data is concentrated in two separate areas rather than around a center.
3. Consider the option with a long tail to the right and most data concentrated on the left. This describes a right-skewed distribution, which is asymmetric because the tail stretches out more on one side.
4. Similarly, the option with a long tail to the left and most data concentrated on the right describes a left-skewed distribution, which is also asymmetric.
5. The option with a single peak in the center and similar frequencies on both sides fits the definition of an approximately symmetric histogram, as the data is balanced around the center.