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

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

Key Concepts

Frequency Distribution

Frequency distribution is a summary of how often different values or ranges of values occur within a dataset. It forms the basis for plots like histograms and cumulative frequency plots, providing insights into the data’s central tendency, dispersion, and overall pattern.

Relationship between Histograms and Cumulative Frequency Plots

The cumulative relative frequency plot is directly derived from the histogram. By summing the frequencies (or relative frequencies) of all bins up to a certain point, one obtains the cumulative distribution. This relationship allows one to interpret and connect the discrete frequency information provided by a histogram with the continuous, accumulating behavior displayed in the cumulative plot.

Histogram

A histogram is a graphical representation of the distribution of numerical data, where data are divided into intervals (bins) and the frequency of data points within each bin is represented by the height of a bar. This visualization helps in understanding the shape, central tendency, and variability of the data.

Cumulative Relative Frequency Plot

A cumulative relative frequency plot is a curve that shows the accumulation of relative frequencies as you move through the dataset. Starting at zero, the plot gradually increases, eventually reaching one (or 100%), which represents the total proportion of the data. This plot is useful for identifying medians, percentiles, and the overall spread of the data.

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