Suppose you are given a histogram representing the number of students in different age groups at a university. The histogram shows a single peak in the middle and the frequencies decrease symmetrically on both sides. Which of the following best describes the shape of this distribution?

• A. Skewed left distribution
• B. Skewed right distribution
• C. Symmetric (bell-shaped) distribution
• D. Uniform distribution

Answer: (C)

Verified step by step guidance

1. Step 1: Understand the key characteristics of the histogram described. It has a single peak in the middle, and the frequencies decrease symmetrically on both sides of this peak.
2. Step 2: Recall the definitions of different distribution shapes: a skewed left distribution has a longer tail on the left side, a skewed right distribution has a longer tail on the right side, a uniform distribution has roughly equal frequencies across all bins, and a symmetric (bell-shaped) distribution has a peak in the center with frequencies decreasing evenly on both sides.
3. Step 3: Compare the histogram's description to these definitions. Since the frequencies decrease symmetrically on both sides of the peak, it does not have a longer tail on either side, ruling out skewed distributions.
4. Step 4: Since the frequencies are not equal across all age groups, the distribution is not uniform.
5. Step 5: Conclude that the distribution is symmetric and bell-shaped, which matches the description of a normal-like distribution with a single central peak and symmetric tails.