Refer to the following five histograms: To which of the...

Refer to the following five histograms:
To which of the above five histograms does the following cumulative relative frequency plot correspond?
(A) $A$
(B) $\underline{B}$
(C) $\mathrm{C}$
(D) $\mathrm{D}$
(E) $\mathrm{E}$

Key Concepts

Histogram

A histogram is a graphical representation of the distribution of numerical data where the data is divided into continuous intervals, known as bins, and the frequency of observations within each bin is represented by the area (or height) of a bar. It provides a visual summary of the data’s distribution, showing features such as central tendency, variability, and skewness.

Relative Frequency

Relative frequency describes the proportion or percentage of the total number of data points that fall within a given interval or category. In the context of a histogram, each bar represents the relative frequency of the data in that range, which allows for comparing distributions regardless of the sample size.

Cumulative Relative Frequency Plot

A cumulative relative frequency plot, also known as an ogive, is a graphical tool that shows the accumulation of relative frequencies up to each class interval. It starts at zero and increases to one (or 100% when expressed as a percentage) and is used to determine medians, percentiles, and to understand the distribution’s overall shape by illustrating how the data accumulate over the range.

Relationship Between Histogram and Cumulative Plot

Understanding the relationship between a histogram and a cumulative relative frequency plot is crucial because the histogram provides a breakdown of how data points are distributed among intervals, while the cumulative plot offers insight into the accumulation of data values. Interpreting both together can help in identifying key distribution characteristics such as where the data concentrates, the rate of accumulation, and potential skewness in the distribution.

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