Question

The question is which box plot has the greatest variability and which box plot has the least variability?

Step 1

**Basics of a boxplot:**

A boxplot is based on the 5-number summary: (Minimum, Q1, Median, Q3, Maximum); Q1 and Q3 are respectively the first and third quartiles.

The lowest^{*} number on the vertical axis, till which the whisker reaches, represents the minimum; the highest^{*} number, till the whisker reaches, represents the maximum.

Of the box, the line/boundary corresponding to the lowest value on the vertical axis, represents Q1; the boundary corresponding to the highest value represents Q3.

The line inside the box represents the median.

The boxplot gives quite a good picture about the central tendency (median), dispersion (range and inter-quartile range), and shape (comparative lengths of the whiskers and relative positions of the median with respect to Q1 and Q3) of the distribution of a dataset. Moreover, it also marks the outliers in the dataset.

^{*}*If there are outliers, then the whiskers may not reach all the way to the outliers, and these would be marked by a symbol, along the line of the whiskers. In that case, the lowest and highest outliers would represent the minimum and maximum values in the dataset, respectively.*

Step 2

**Description:**

The inter-quartile range or IQR is: IQR = (Q3 – Q1).

It is a simple measure of dispersion or variability in the dataset, which provides the range within which, the middle-most 50% of the observations lie.

Although the IQR is not readily displayed on a boxplot, it can be calculated quite easily, simply by identifying Q1...

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