Question

mel and hailey are comparing the number of texts they each send per week. they each decide to look over their text logs and count their weekly sent texts over the past year. these data sets are then compiled into the following box plots:

texts sent throughout year
box plot for mel and hailey, x - axis: weekly sent messages (10 to 80)

based on these box plots, choose all of the following statements that are true.

show your work here

the maximum number of texts for mel is equal to the maximum number of texts for hailey.

the median number of texts for hailey is 15 larger than the median value for mel.

the range in the number of texts is larger for hailey than for mel.

the range in the number of texts is larger for mel than for hailey.

the minimum number of texts that mel sent is greater than the minimum number of texts hailey sent.

Explanation:

To solve this, we analyze each statement using box - plot components (minimum, Q1, median, Q3, maximum) and range (maximum - minimum).

Step 1: Analyze "The maximum number of texts for Mel is equal to the maximum number of texts for Hailey."

From the box - plots, we can see that the right - most whisker (representing the maximum value) for both Mel and Hailey ends at the same point on the "Weekly sent messages" axis. So, the maximum number of texts for Mel is equal to the maximum number of texts for Hailey. This statement is true.

Step 2: Analyze "The median number of texts for Hailey is 15 larger than the median value for Mel."

The median is represented by the line inside the box. Looking at the box - plots, the median of Mel seems to be around 50 and the median of Hailey seems to be around 45 (or vice - versa depending on the exact plot, but the difference is not 15). So, this statement is false.

Step 3: Analyze "The range in the number of texts is larger for Hailey than for Mel."

The range is calculated as \( \text{Range}=\text{Maximum}-\text{Minimum} \). For Mel, let's assume the minimum is around 20 and the maximum is around 80, so the range is \( 80 - 20=60 \). For Hailey, if the minimum is around 30 and the maximum is around 80, the range is \( 80 - 30 = 50 \). So the range of Mel is larger than that of Hailey. Thus, this statement is false.

Step 4: Analyze "The range in the number of texts is larger for Mel than for Hailey."

As calculated above, for Mel, if minimum \( = 20 \) and maximum \( = 80 \), range \( = 80 - 20=60 \). For Hailey, if minimum \( = 30 \) and maximum \( = 80 \), range \( = 80 - 30 = 50 \). Since \( 60>50 \), the range of Mel is larger than that of Hailey. This statement is true.

Step 5: Analyze "The minimum number of texts that Mel sent is greater than the minimum number of texts Hailey sent."

From the box - plots, the left - most whisker (representing the minimum value) of Mel is to the right of the left - most whisker of Hailey. This means that the minimum number of texts Mel sent is greater than the minimum number of texts Hailey sent. This statement is true.

Answer:

• The maximum number of texts for Mel is equal to the maximum number of texts for Hailey.
• The range in the number of texts is larger for Mel than for Hailey.
• The minimum number of texts that Mel sent is greater than the minimum number of texts Hailey sent.