Final answer:
The statement that a histogram can be constructed for both quantitative and qualitative data is false. A histogram represents the frequency of quantitative data through contiguous bars, with the x-axis showing data intervals and the y-axis showing their frequency. Qualitative data is best represented by bar graphs or pie charts.
Step-by-step explanation:
A histogram can be constructed for data that are quantitative, but not for qualitative data. The statement is false. A histogram is a type of graph that represents the frequency distribution of quantitative data. It consists of contiguous bars whose heights correspond to the frequency values. The horizontal axis, or x-axis, denotes the data classes or intervals, while the vertical axis, or y-axis, represents the frequency of the data within those classes.
When constructing a histogram, the data involved must be quantitative and often continuous. For example, the heights of individuals in a group measured to the nearest half-inch constitute quantitative data and can be represented in a histogram, showing how many individuals fall into various height ranges.
On the other hand, qualitative or categorical data, like colors or types of fruit, are better represented using bar graphs or pie charts. In qualitative data, the categories do not have a natural order or numerical value, and thus, histograms are not suitable.
Therefore, when deciding on the best graphical representation, the type of data (quantitative or qualitative) is a crucial consideration. For quantitative continuous data, a histogram is an appropriate choice.