Final answer:
To create a histogram with intervals of width 1, the first bar's range is centered on the data point, such as 31. The tallest bar indicates the class interval with the highest frequency, and the interval with the median is where cumulative frequency is half of the total. A histogram effectively shows the distribution of continuous data.
Step-by-step explanation:
To construct a histogram of a data set where each interval has width 1, you would start with determining the range of the first bar and its central point. If you have a data value of 31, then the first bar would likely range from 30.5 to 31.5, with 31 being the central point.
The widths of the other bars would also be 1, with each central point being at the middle value of the respective class interval. The tallest bar in the histogram will correspond to the class interval with the highest frequency, and its height will reflect the number of data points within that interval.
The class interval containing the median would be the one where the cumulative frequency reaches 50% of the total data points. A smooth curve through the midpoints of the tops of the bars can represent the approximate distribution of the data visually, highlighting whether the data is normally distributed, skewed, or has outliers.
When presenting data such as the median household income for a city, a histogram is typically better than a bar graph because it shows the distribution of a continuous data set.