Question

unit 4 test: graphs and describing distributions multiple cho

1. the five numbers used on a box and whisker plot are

(a) the five smallest observations.
(b) the five largest observations.
(c) the mean, the median, the maximum, the standard deviation and the sample size.
(d) ( x_1, x_2, x_3, x_4 ), and ( x_5 ).
(e) the median, the quartiles, the minimum and the maximum.
○ a
○ b
○ c
○ d
○ e

Explanation:

A box - and - whisker plot (also known as a box plot) is constructed using the five - number summary of a data set. The five - number summary consists of the minimum value (the smallest data point in the set), the first quartile (\(Q_1\), the value that separates the lowest 25% of the data from the rest), the median (\(Q_2\), the middle value of the data set), the third quartile (\(Q_3\), the value that separates the lowest 75% of the data from the highest 25%), and the maximum value (the largest data point in the set).

• Option (a): The five smallest observations do not form the basis of a box - and - whisker plot. A box - and - whisker plot is about summary statistics of the entire data set, not just the smallest values.
• Option (b): Similarly, the five largest observations are not the components of a box - and - whisker plot.
• Option (c): The mean and standard deviation are not part of the five - number summary used for a box - and - whisker plot. The five - number summary focuses on positional values (minimum, quartiles, median, maximum) rather than measures of central tendency (mean) and dispersion (standard deviation) in this context.
• Option (d): \(x_1,x_2,x_3,x_4,x_5\) is a rather vague and non - standard representation. It does not correspond to the well - defined five - number summary.
• Option (e): This option correctly lists the median, the quartiles (first and third), the minimum, and the maximum, which are the exact components of the five - number summary used to create a box - and - whisker plot.

Answer:

E. The median, the quartiles, the minimum and the maximum.