Which of the following statements about histograms is true?
a. A histogram may be used as a graphical display of categorical data.
b. A histogram generally has no gaps between rectangles, because it is a graphical display of a numerical variable and the horizontal axis follows a number scale.
c. A histogram shows the relative frequencies of nominal data.
d. A histogram may be used as a graphical display of ordinal data.
The correct answer and explanation is:
The correct answer is:
b. A histogram generally has no gaps between rectangles, because it is a graphical display of a numerical variable and the horizontal axis follows a number scale.
Explanation:
A histogram is a type of bar graph used to represent the distribution of numerical (quantitative) data. Its main purpose is to show the frequency or relative frequency of data values falling within specific intervals, called bins or classes.
- Why no gaps?
Unlike bar charts for categorical data, histograms typically do not have gaps between the bars. This is because the horizontal axis represents a continuous number scale, where the data values flow seamlessly from one interval to the next. The bars represent ranges of values, and the adjacent intervals naturally connect without breaks. - Why numerical data?
Histograms are specifically designed for numerical data that can be ordered and measured on a continuous scale (e.g., height, weight, test scores). The bins group these numerical values to reveal the shape of the distribution (e.g., normal, skewed, uniform). - Categorical data and histograms
Statement (a) is incorrect because histograms are not used for categorical data. For categorical data (such as colors, types of fruit, or nominal variables), bar charts with gaps between bars are appropriate, since categories are distinct and non-numeric. - Nominal and ordinal data
Nominal data have categories with no natural order, so you can’t display their distribution with a histogram (statement c is false).
Ordinal data have a meaningful order but do not necessarily have numeric intervals; while sometimes ordinal data might be displayed in bar charts, histograms are generally reserved for numerical data (statement d is false).
Summary:
- Histograms are for numerical data.
- Bars touch each other, representing continuous intervals.
- They reveal the shape and frequency distribution of data.
- For categorical data, bar charts (with gaps) are used instead.
This makes statement b the correct and best description of histograms.