A dot plot shows the number of shirts sold in each size: Small ($3$ dots), Medium ($5$ dots), Large ($2$ dots), and Extra Large ($4$ dots). Which histogram best represents the same data?

• A. A histogram with four bars labeled Small, Medium, Large, and Extra Large, with heights $5$, $3$, $4$, and $2$ respectively.
• B. A histogram with four bars labeled Small, Medium, Large, and Extra Large, with heights $3$, $5$, $2$, and $4$ respectively.
• C. A histogram with two bars labeled Small/Medium and Large/Extra Large, both with height $7$.
• D. A histogram with four bars labeled Small, Medium, Large, and Extra Large, all with equal heights.

Answer: (B)

Verified step by step guidance

1. Step 1: Understand the data from the dot plot. Each dot represents one shirt sold, so count the dots for each size: Small has 3 dots, Medium has 5 dots, Large has 2 dots, and Extra Large has 4 dots.
2. Step 2: Recall that a histogram represents data with bars where the height of each bar corresponds to the frequency (or count) of each category or interval.
3. Step 3: Match each size category to a bar in the histogram, ensuring the height of the bar equals the number of shirts sold for that size. For example, the bar for Small should have height 3, Medium should have height 5, Large should have height 2, and Extra Large should have height 4.
4. Step 4: Compare the given histogram options to the frequencies you identified. The correct histogram will have bars labeled Small, Medium, Large, and Extra Large with heights exactly matching the counts from the dot plot.
5. Step 5: Eliminate histograms that do not match these frequencies, such as those with incorrect bar heights or combined categories, to identify the histogram that best represents the original data.