a data set has a median of 12, an upper quartile of 15, a lower quartile of 10, a minimum of 4, and a…

a data set has a median of 12, an upper quartile of 15, a lower quartile of 10, a minimum of 4, and a maximum of 20. which statement is true of the box plot of this data set? the box will go from 10 to 12. a line dividing the box will be at 12. the left whisker will go from 4 to 15. the right whisker will go from 12 to 20.

a data set has a median of 12, an upper quartile of 15, a lower quartile of 10, a minimum of 4, and a maximum of 20. which statement is true of the box plot of this data set? the box will go from 10 to 12. a line dividing the box will be at 12. the left whisker will go from 4 to 15. the right whisker will go from 12 to 20.

Answer

Explanation:

Step1: Recall box - plot components

In a box - plot, the box extends from the lower quartile ($Q_1$) to the upper quartile ($Q_3$), and a line inside the box represents the median. The left whisker extends from the minimum value to the lower quartile, and the right whisker extends from the upper quartile to the maximum value. Given $Q_1 = 10$, $Q_3=15$, median $= 12$, minimum $ = 4$, maximum $=20$.

Step2: Analyze each option

  • Option 1: The box goes from $Q_1 = 10$ to $Q_3 = 15$, not from 10 to 12.
  • Option 2: The line dividing the box represents the median. Since the median is 12, a line dividing the box will be at 12. This is correct.
  • Option 3: The left whisker goes from the minimum (4) to the lower quartile (10), not from 4 to 15.
  • Option 4: The right whisker goes from the upper quartile (15) to the maximum (20), not from 12 to 20.

Answer:

A line dividing the box will be at 12.