The histogram to the right represents the weights $w$ (in kilograms $\mathrm{kg}$) of a group of students. Which of the following statements is most likely true about the distribution of weights shown in the histogram?

• A. The distribution is approximately symmetric, with most weights clustered around the center $w$.
• B. The distribution is uniform, with all weight intervals having the same frequency $f$.
• C. The distribution is left-skewed, with a long tail on the left side.
• D. The distribution is bimodal, with two distinct peaks at the extremes.

Answer: (A)

Verified step by step guidance

1. Step 1: Understand the types of distributions mentioned in the problem. A symmetric distribution has a roughly equal shape on both sides of the center. A uniform distribution has all intervals with approximately the same frequency. A left-skewed distribution has a longer tail on the left side, meaning more values are spread out toward lower weights. A bimodal distribution has two distinct peaks or modes.
2. Step 2: Examine the histogram carefully to identify the shape of the distribution. Look for where the highest bars (frequencies) are located and whether the bars decrease evenly on both sides or if there is a tail on one side.
3. Step 3: Check if the frequencies are roughly the same across all weight intervals. If yes, the distribution is uniform. If not, move to the next step.
4. Step 4: Determine if the histogram has one peak (unimodal) or two peaks (bimodal). If there are two distinct high points separated by lower frequencies, it is bimodal.
5. Step 5: Assess the symmetry by comparing the left and right sides of the peak. If the bars decrease evenly on both sides, the distribution is symmetric. If the tail extends more to the left, it is left-skewed. Based on this, select the statement that best matches the observed shape.