Question

1. the box plot below shows the number of siblings each student in mrs. hines class has. which of the following statements is not true? a. the interquartile range of the data is approximately 2. b. the median number of siblings each student has is approximately 1.75. c. there is at least one student who has no siblings. d. over half of the students in mrs. hines class have two or more siblings.

Explanation:

Step1: Recall box - plot concepts

In a box - plot, the inter - quartile range (IQR) is the difference between the third quartile ($Q_3$) and the first quartile ($Q_1$). The median is the middle value.

Step2: Analyze the box - plot

For the given box - plot of the number of siblings:
The lower quartile ($Q_1$) is approximately 1, and the upper quartile ($Q_3$) is approximately 3. So, the IQR=$Q_3 - Q_1=3 - 1 = 2$.
The median is approximately 2.
Half of the data lies between $Q_1$ and $Q_3$. Looking at the box - plot, we can see that less than half of the students have 2 or more siblings.

Step3: Evaluate each option

• Option A: The inter - quartile range is $Q_3 - Q_1$. From the box - plot, $Q_1\approx1$ and $Q_3\approx3$, so $IQR = 3 - 1=2$. This statement is true.
• Option B: The median of the box - plot is approximately 2. This statement is true.
• Option C: There are students with 0, 1, 2, 3, 4, 5 siblings. There are students with at least 1 sibling. This statement is true.
• Option D: The box - plot shows that the number of students with 2 or more siblings is less than half of the students. This statement is false.

Answer:

D. Over half of the students in Mrs. Hines' class have two or more siblings.