Question

The dot plot represents a sampling of ACT scores:

Answer 1

The data from a dot plot can be analyzed to find the five number summary, from which a box plot can be constructed

The correct option for the details of the box plot that represents the dot plot data is;

Box plot titled ACT Score with a minimum of 18, quartile 1 of 21, median of 22, quartile 3 of 23, and maximum of 25

The process of deriving the five number summary of the box plot above is as follows;

Known:

The data from the dot plot can be expressed in increasing order for analysis of a box plot as follows;

18, 19, 19, 19, 21, 21, 21, 21, 22, 22, 22,22, 23, 23, 23, 24, 24, 25

The number of data points in the statistics, n = 18

Unknown:

The five number summary

Method:

Finding the five number summary as follows;

The minimum value = 18

The maximum value = 25

• The first quartile, inclusive of the median Q₁ = The middle number of the lower half {18, 19, 19, 19, 21, 21, 21, 21, 22} = The (9 + 1)/2 th term

∴ Quartile 1 = Q₁ = 5th term = 21

• The second quartile, Q₂ = The median (the middle number) = (22 + 22)/2 = 22 = Quartile 2

Quartile 2 = 22

• The third quartile = The middle number of the upper half {22, 22,22, 23, 23, 23, 24, 24, 25} = Quartile 3 = 23

Quartile 3 = 23

Combining the above 5 number summary, the correct option for the box plot representing the dot plot data, is therefore;

Box plot titled ACT Score with a minimum of 18, quartile 1 of 21, median of 22, quartile 3 of 23, and maximum of 25

Learn more about box and whiskers, and dot plots here;

brainly.com/question/4002977