Use the side-by-side box plots shown to answer the questions...

Use the side-by-side box plots shown to answer the questions that follow. (a) To the nearest integer, what is the median of variable $x$ ? (b) To the nearest integer, what is the first quartile of variable $y ?$ (c) Which variable has more dispersion? Why? (d) Does the variable $x$ have any outliers? If so, what is the value of the outlier(s)? (e) Describe the shape of the variable $y$. Support your position.

Use the side-by-side box plots shown to answer the questions that follow.
(a) To the nearest integer, what is the median of variable $x$ ?
(b) To the nearest integer, what is the first quartile of variable $y ?$
(c) Which variable has more dispersion? Why?
(d) Does the variable $x$ have any outliers? If so, what is the value of the outlier(s)?
(e) Describe the shape of the variable $y$. Support your position.

Key Concepts

Distribution Shape

The shape of a distribution describes the symmetry or skewness of the data. A symmetric distribution shows a balanced spread around the median, while a skewed distribution displays a longer tail on one side. Box plots can provide insights into the shape by comparing the positions of Q1, the median, and Q3 and the lengths of the whiskers.

Outliers

Outliers are data points that fall significantly outside the overall pattern of the dataset and are markedly distant from other observations. In box plot representations, outliers are typically indicated by individual points that lie beyond the whiskers, which are drawn to a specified distance from the quartiles.

Dispersion

Dispersion refers to the degree of spread in a dataset. In box plots, dispersion is visually represented by the length of the box (IQR) and the range covered by the whiskers. Comparing these elements across different plots can reveal which dataset has greater variability.

Quartiles

Quartiles are values that divide an ordered dataset into four equal segments. The first quartile (Q1) represents the 25th percentile, and the third quartile (Q3) represents the 75th percentile. They are essential in identifying the spread and central concentration of the data, and are used to calculate the interquartile range (IQR).

Median

The median is the middle value of an ordered dataset that divides it into two equal parts. In box plots, it is typically depicted as a line within the box, and it provides a measure of central tendency that is robust to outliers.

Box Plots

Box plots are graphical representations that summarize the distribution of a dataset using five key statistics: the minimum, first quartile (Q1), median, third quartile (Q3), and maximum. They often include markers for outliers. Side?by?side box plots allow for easy comparison of these statistics across different variables or groups.

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