Question

Select all statements that must be true.

(Select all that apply)
Students selecting B are likely mistaking the range for
the IQR. Students selecting C are likely mistaking the
median for the IQR. Students selecting D are likely
mistaking the mean for the median. It may be possible
that the mean is 3.6 goals per game, but cannot be
determined from the box plot alone. Students selecting
F are likely mistaking Q1 for the minimum.
A. The interquartile range (IQR) is 1.2 goals per game.
B. The interquartile range (IQR) is 3.2 goals per game.
C. The interquartile range (IQR) is 3.6 goals per game.
The average goals scored per game are calculated for
20 soccer tournaments. The 20 averages are used to
create this box plot.
O O OOO
D. The mean is 3.6 goals per game.
E. The median is 3.6 goals per game.
E The minimum is 2.8 goals per game.
H
G. The maximum is 5.6 goals per game.
2
2.4 2.8 3.2 3.6
4
4.4
4.8
5.2 5.6
6
Average Number of Goals per
Game

Answer 1

The maximum = 5.6 goals per game

median = 3.6 goals per game

Interquartile range (IQR ) = 1.2 goals per games

Step-by-step explanation:

To solve this question, we need an illustration that identifies the part of the box and whiskers plot:

The minimum on the box and whiskers = 2.4 goals per game

The maximum = 5.6 goals per game

The median = the line in between the box

median = M on the image

median = 3.6 goals per game

upper quartile = Q3 = 4

lower quartile = Q1 = 2.8

The interquartile range = IQR

`\begin{gathered} \text{IQR = Q}_3-Q_1 \\ \text{IQR = }4\text{ - 2.8} \\ \text{IQR = 1.2} \end{gathered}`

Interquartile range (IQR ) = 1.2 goals per games

`\begin{gathered} \text{Mean = average of the data set} \\ \text{Mean = }\frac{su\text{m of the numbers}}{nu\text{mber of the data set}} \\ \text{Mean = }\frac{2.4\text{ + }2.8+3.6+4+5.6}{5} \\ \text{Mean = 18.4/5} \\ \text{Mean = 3.68} \end{gathered}`

The mean is 3.68 goals per game