Question

Which data set could be represented by the box plot shown below? A horizontal boxplot is plotted along a horizontal axis marked from 14 to 30, in increments of 1. A left whisker extends from 16 to 18. The box extends from 18 to 26 and is divided into 2 parts by a vertical line segment at 22. The right whisker extends from 26 to 28. All values estimated.

Answer 1

Answer:

Therefore any set of data that satisfies the 5-Number summary: 16,18,22,26 and 28 can be represented with the box plot.

Step-by-step explanation:

Interpreting Box Plots

We use a box plot to present the 5-Number summary of a set of data.

The values contained in the 5-Number summary are:

• Minimum Value
• First Quartile
• Median
• Third Quartile,
• Maximum Value

In the box plot, the following rules apply:

• 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 16 to 18, therefore:

• Minimum Value=16
• First Quartile =18

The box extends from 18 to 26 and is divided into 2 parts by a vertical line segment at 22.

• Median=22
• Thrid Quartile=26

The right whisker extends from 26 to 28.

• Maximum Value =28

Therefore any set of data that satisfies the 5-Number summary: 16,18,22,26 and 28 can be represented with the box plot.

Answer 2

Box plot has boxes with some lines ( called whiskers ).

Box plot on the graphical level tells about 5 points:

1.    Minimum (Q0 or 0th percentile),
2.    Maximum (Q4 or 100th percentile),
3.    Median (Q2 or 50th percentile),
4.    First quartile (Q1 or 25th percentile),
5.    Third quartile (Q3 or 75th percentile).

There is starting whisker or left whisker denoting point minimum (Q0) and extends from there the line to Q1 ( first quartile).

Then the box starts which starts from Q1 and touched Q3. In the middle it passes through Q2 ( The median of the data ), and thus has a line in it.

At last, there is end whisker or right whisker denoting end quantile or Q4 (the maximum point).

Given data:

Left whisker extends from 16 to 18.

     Thus Q0 = 16

              Q1 = 18

Box plot starts from 18 and extends to 26, and is split by a vertical line segment at 22.

    Thus Q2 = 22

             Q3 = 26

The right whisker or end whisker extends from 26 to 28

    Thus Q4 = 28.

Thus the description of data is given as:

$Q_0 = Minimum = 16\\Q_1 = First\: quartile = 18\\Q_2 = Second \:quartile = Median= 22\\Q_3 = Third\: quartile = 26\\Q_4 = Maximum = 28$

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