A graph of a data set, composed of a series of rectangles, each proportional in width to the range of values in a class and proportional in height to the number of items or fraction of items falling in these classes, is called which of the following?

The question provides the precise definition of a histogram. A histogram is a graphical tool used to represent the frequency distribution of a set of continuous or discrete data. It is constructed by dividing the range of data into a series of intervals (classes or bins) of equal width. For each interval, a rectangle is drawn. The height of the rectangle is proportional to the frequency—the number of observations falling into that class. This visual representation helps in understanding the data's underlying distribution, central tendency, and spread.

B. Raw data: This refers to the unprocessed, unorganized collection of information before any statistical analysis or graphical representation is performed.
C. Ogive: This is a cumulative frequency polygon, a line graph that plots cumulative frequencies, not a bar graph of class frequencies.
D. Venn diagram: This uses overlapping circles to show the logical relationships and commonalities between different sets, not a frequency distribution.

1. Montgomery, D. C. (2020). Introduction to statistical quality control (9th ed.). Wiley. In Chapter 5, "Descriptive Statistics," Section 5-3, "The Histogram," it is defined as: "To construct a histogram, we must divide the range of the data into intervals... The vertical axis is the frequency... and a rectangle is drawn over each class interval with height equal to the class frequency." (p. 169).

2. Laman, S. A., & Westfall, L. K. (Eds.). (2023). The Certified Quality Engineer Handbook (5th ed.). ASQ Quality Press. Chapter 23, "Basic Statistical Methods," describes a histogram as "a bar chart that shows the frequency distribution of a data set... The height of each bar represents the frequency of values in that class." (p. 336).

3. Penn State Eberly College of Science. (n.d.). STAT 200: Elementary Statistics. Lesson 2: Summarizing Data Graphically and Numerically. Retrieved from https://online.stat.psu.edu/stat200/lesson/2/2.2/2.2.2. In Section 2.2.2, "Histograms," it states, "A histogram is a graph that uses bars to portray the frequencies or the relative frequencies of the possible outcomes for a quantitative variable."