Question

A movie theater recorded the number of tickets sold daily for a popular vampire movie during the month of december. The box plot shows the data for the number of the tickets sold, in the hundreds

Answer 1

Answer and Explanation:

Given:

The box plot showing the data for the number of the tickets sold, in hundreds as shown below;

Recall that a box plot is generally given as below;

If we compare the above with the given box plot we can see that the;

Minimum Value = 100

First Quartile(Q1) = 300

Median = 400

Third Quartile (Q3) = 600

Maximum Value = 900

Q1(first quartile) is at 300 and the median, which is the middle number is at 400. Note that the Q1 represents the value under which 25% of the data points are found when they are arranged in increasing order. So 25% of the data are below 300 and are between the first quartile and the median.

25% of the data is between 300 and 400. TRUE

Recall that the interquartile range(IQR) is the difference between the third quartile and the first quartile, so we'll have;

`\begin{gathered} IQR=Q3-Q1 \\ =600-300 \\ =300 \end{gathered}`

So the IQR is 300 and not 800.

The interquartile range is 800. FALSE

As earlier mentioned above, the median is 400. TRUE

As earlier mentioned above, the first quartile is 300. TRUE

Note that the range is the difference between the maximum value and the minimum value, so we'll have;

`\begin{gathered} Range=Maximum\text{ value}-Minimum\text{ value} \\ =900-100 \\ =800 \end{gathered}`

So we can see from the above that the range is 800 and not 300.

The range is 300. FALSE

Note that 25% of the data are between Q1 and the median and 25% of the data are also between the median and the Q3, so we have that 50% of the data are between Q1 and Q3

50% of the data are between 300 and 600. TRUE

The minimum value is 100. TRUE

The maximum value is 9. FALSE