Final answer:
The statement is false; in a histogram for discrete numerical data, the bars should not have spaces between them to represent the frequency of each class or bin accurately.
Step-by-step explanation:
The statement is false. When constructing a histogram for discrete numerical data, the bars should touch each other. This is because a histogram displays the frequency distribution of quantitative measures, and the bars represent the frequency of each class or bin. For discrete data, the bins represent distinct categories or values, which are directly next to each other on the number line. Therefore, there is no need for spaces between the bars.
However, for a bar graph that represents categorical data, there should be spaces between the bars to show the distinct categories. In summary, histograms for discrete data do not have spaces between the bars, while bar graphs for categorical data do.
To construct a histogram, it is important to select an appropriate number and width of the bins to ensure the clarity of the displayed information. The histogram is used to visualize the shape, center, and spread of the data, and it can highlight the distribution of the data, such as if it is normal, skewed, or otherwise.