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;
<em>Box plot </em><em>titled ACT Score with a minimum of </em><em>18</em><em>, quartile 1 of </em><em>21</em><em>, median of </em><em>22</em><em>, quartile 3 of </em><em>23</em><em>, and maximum of </em><em>25</em>
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, <u>22, 22</u>, 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, <u>22}</u> = 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 {<u>22</u>, 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
