To determine which statement about the mean and median is most likely true for the given data, let's start by constructing and analyzing the histogram for the bedroom areas.
1. Interpret the frequency table:
- [tex]$60 \leq A < 80$[/tex]: 4 bedrooms
- [tex]$80 \leq A < 100$[/tex]: 6 bedrooms
- [tex]$100 \leq A < 120$[/tex]: 5 bedrooms
- [tex]$120 \leq A < 140$[/tex]: 3 bedrooms
- [tex]$140 \leq A < 160$[/tex]: 1 bedroom
2. Construct the histogram:
- The x-axis will represent the bedroom areas divided into intervals: [60-80), [80-100), [100-120), [120-140), and [140-160).
- The y-axis will represent the number of bedrooms within each interval.
3. Plotting the histogram:
- For the interval 60-80, there are 4 bedrooms.
- For the interval 80-100, there are 6 bedrooms.
- For the interval 100-120, there are 5 bedrooms.
- For the interval 120-140, there are 3 bedrooms.
- For the interval 140-160, there is 1 bedroom.
4. Analyze the histogram:
- Most bedrooms fall in the intervals 80-100 and 100-120.
- There's a noticeable drop-off after the 120-140 interval, with very few bedrooms in the 140-160 range.
- Since there are fewer data points in the higher intervals compared to the lower and middle intervals, the histogram tail will extend to the right, indicating right skewness.
5. Determine the mean and median:
- In a right-skewed distribution, the tail is on the right side. This generally means that the data has higher values pulling the mean upwards more than the median, which is more centrally located.
Therefore, the statement that is most likely true is:
The histogram is right-skewed, so the mean is greater than the median.
