Question

the students in marlys math class recorded the dimensions of their bedrooms in a frequency table.

bedroom areas
\

$$\begin{array}{|c|c|} \\hline \\text{area (sq. ft)} & \\text{number of bedrooms} \\\\ \\hline 60 \\le a < 80 & 4 \\\\ \\hline 80 \\le a < 100 & 6 \\\\ \\hline 100 \\le a < 120 & 5 \\\\ \\hline 120 \\le a < 140 & 3 \\\\ \\hline 140 \\le a < 160 & 1 \\\\ \\hline \\end{array}$$

create a histogram to represent the data. which statement is most likely true about the mean and the median of the data?

• the histogram is right-skewed, so the mean is less than the median.
• the histogram is right-skewed, so the mean is greater than the median.
• the histogram is left-skewed, so the mean is less than the median.
• the histogram is left-skewed, so the mean is greater than the median.

Explanation:

Analyze the frequency distribution

The frequency of bedroom areas decreases as the area increases:

• \(60 \le A < 80\): 4
• \(80 \le A < 100\): 6 (peak)
• \(100 \le A < 120\): 5
• \(120 \le A < 140\): 3
• \(140 \le A < 160\): 1

Determine the shape of the distribution

The peak is on the left side (\(80 \le A < 100\)), and the tail extends to the right (larger values). This indicates a right-skewed distribution.

Compare the mean and median

In a right-skewed distribution, the mean is typically pulled toward the longer tail on the right, making the mean greater than the median.

Answer:

• The histogram is right-skewed, so the mean is less than the median.
• The histogram is right-skewed, so the mean is greater than the median. (Correct answer)
• The histogram is left-skewed, so the mean is less than the median.
• The histogram is left-skewed, so the mean is greater than the median.