Final answer:
A histogram displays data by grouping numbers into ranges. Each range (or bin) is graphically represented as a bar, and the area of the bar is proportional to the frequency of data points within that range. Intervals are chosen carefully, and data on boundaries are included in the left interval except for the extreme right boundary.
Step-by-step explanation:
The student's question revolves around the concept of a histogram and how to represent a data set on a number line through intervals. A histogram is a graphical representation that organizes a group of data points into user-specified ranges. Similar to a bar chart, a histogram plots the frequency of data points within these ranges or intervals. The intervals have endpoints, and each bar's height corresponds to the frequency of data within the interval.
When constructing a histogram, one must decide on the number of intervals, also called bins, and then calculate the range for each. This is done by subtracting the smallest value from the largest value and dividing by the number of intervals. Each interval's endpoint is calculated by adding the interval width to the previous interval's endpoint. Data values that fall on an interval boundary are typically included in the interval to the left, except for the rightmost boundary.
Midpoints are used to represent the data points of each interval. For example, for an interval of 49.5-59.5, the midpoint is 54.5. In a skewed distribution, one side of the histogram does not mirror the other side, indicating the direction in which the data is skewed.