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Which data set could be represented by the box plot shown below?


A horizontal boxplot is plotted along a horizontal axis marked from 0 to 20, in increments of 1. A left whisker extends from 1 to 6. The box extends from 6 to 16 and is divided into 2 parts by a vertical line segment at 12. The right whisker extends from 16 to 19. All values estimated.

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Answer:

Any set of data that satisfies the 5-Number summary: 1,6,12,16 and 19 can be represented with the box plot.

Step-by-step explanation:

Interpreting Box Plots

A box plot is used to present the 5-Number summary of a set of data.

The 5-Number summary consists of the following in their order of appearance on the box plot.

  • Minimum Value
  • First Quartile, [tex]Q_1[/tex]
  • Median, [tex]Q_2[/tex]
  • Third Quartile, [tex]Q_3[/tex]
  • Maximum Value

In the box plot, the following rules applies

  • The whisker starts from the minimum value and ends at the first quartile.
  • The box starts at the first quartile and ends at the third quartile. There is a vertical line inside the box which shows the median.
  • The end whisker starts at the third quartile and ends at the maximum value.

Using these, we interpret the given box plot

A left whisker extends from 1 to 6.

  • Minimum Value=1
  • First Quartile =6

The box extends from 6 to 16 and is divided into 2 parts by a vertical line segment at 12.

  • Median=12
  • Thrid Quartile=16

The right whisker extends from 16 to 19.

  • Maximum Value =19

Therefore any set of data that satisfies the 5-Number summary: 1,6,12,16 and 19 can be represented with the box plot.

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