Final answer:
A histogram's first class interval is based on the smallest data value and a consistent width, which is followed by the subsequent intervals. The tallest bar indicates the interval with the highest frequency. The median is in the interval where the cumulative frequency reaches half of the total number of data points, and by drawing a smooth curve through the midpoints of the bars, you can describe the shape of the distribution.
Step-by-step explanation:
To construct a histogram of a data set, starting with the first bar, you will determine your class intervals, which are ranges of data that each bar represents. The range of the first bar depends on the smallest data value and the width of your intervals. If each interval has width 1, and considering your first data point, your first bar will have a range from that data point minus 0.5 to that data point plus 0.5. The central point of that bar would be the data point itself. For the other bars, maintain a consistent width of 1 and establish central points that are sequential whole numbers from the first central point.
The tallest bar in the histogram will correspond to the interval with the highest frequency, meaning it contains the largest number of data points. To find its height, count the number of data points that fall within that interval. For a histogram depicting median household income, the heights of the bars will represent how many households fall within each income range. Since histograms are suited to display the distribution and frequencies of data, it will be a better choice than a bar graph, which is usually used for comparing distinct, non-continuous categories.
The median of the data set can be located by finding the class interval that would contain the middle value when all the data points are listed in ascending order. Since histograms depict frequencies, the class interval that holds the median would have a cumulative frequency that reaches half the total number of data points.
Describing the shape of your histogram, you must note whether it is symmetrical, skewed to the right, skewed to the left, bimodal, or uniform. For example, if most bars are on the left and the heights decrease as you move right, then it is skewed to the right. By drawing a smooth curve through the midpoints of the tops of the bars, you get a visual representation of the data's distribution shape, which helps in identifying the approximate distribution.