mr. banner recorded the amount of time each of his students studied for the math test. the box - plot shows…

mr. banner recorded the amount of time each of his students studied for the math test. the box - plot shows the summary of the\nstudy time\namount (minutes)\nwhich statement best describes the data represented in the box - plot?\na the mean number of minutes the students studied is 45.\nb the greatest number of students studied is 45.\nc half the students studied from 35 to 45 minutes.\nd the data represent 45 study time amounts.

Answer

Explanation:

Step1: Recall box - plot properties

A box - plot shows the five - number summary: minimum, first quartile ($Q_1$), median ($Q_2$), third quartile ($Q_3$), and maximum. The box represents the inter - quartile range (IQR) from $Q_1$ to $Q_3$, and half of the data lies within this range.

Step2: Analyze each option

Option A: The box - plot does not show the mean. We cannot determine the mean from the box - plot alone.
Option B: The greatest number of minutes the students studied is the maximum value on the box - plot, which is 90, not 45.
Option C: The box represents the middle 50% of the data. The lower end of the box is $Q_1$ and the upper end is $Q_3$. But from the box - plot, $Q_1 = 45$ and $Q_3=70$, not from 35 to 45.
Option D: The box - plot shows the distribution of study times. The entire range of data from the minimum (30) to the maximum (90) represents all the study - time amounts. And half of the data lies from the first quartile (45) to the maximum (90) in terms of the spread of the box and the upper whisker.

Answer:

D. The data represent 45 study time amounts.