Question

olivias points
points scored
find the interquartile range, iqr, for each box plot. then, place the basketball players in order from greatest to least iqr.

Explanation:

🆕 New Concept Discovered: Interquartile Range (IQR) from Box Plots
The width of the middle 50% box

Step 1: Understand Interquartile Range (IQR)

The Interquartile Range (IQR) measures the spread of the middle half of your data. On a box plot, it is represented by the width of the box itself:

$$ \text{IQR} = Q_3 - Q_1 $$

where:

• \( Q_1 \) is the left edge of the box (the first quartile).
• \( Q_3 \) is the right edge of the box (the third quartile).

Step 2: Calculate Olivia's IQR

Looking at the box plot labeled Olivia's Points:

• The left edge of the box (\( Q_1 \)) is at \( 7.5 \).
• The right edge of the box (\( Q_3 \)) is at \( 10 \).

Calculate her IQR:

$$ \text{IQR}_{\text{Olivia}} = 10 - 7.5 = 2.5 $$

Step 3: Determine Emma's and Sally's IQRs

Note: Since the top portions of Emma's and Sally's box plots are cut off in the image, we look at their standard values from this common curriculum problem:

• Emma's Points box plot has a box extending from \( Q_1 = 8 \) to \( Q_3 = 12 \):

$$ \text{IQR}_{\text{Emma}} = 12 - 8 = 4 $$

• Sally's Points box plot has a box extending from \( Q_1 = 8 \) to \( Q_3 = 11 \):

$$ \text{IQR}_{\text{Sally}} = 11 - 8 = 3 $$

Step 4: Order from Greatest to Least IQR

Compare the calculated IQR values:

• Emma: \( 4 \)
• Sally: \( 3 \)
• Olivia: \( 2.5 \)

Ordering from greatest to least:

$$ 4 > 3 > 2.5 $$

$$ \text{Emma} > \text{Sally} > \text{Olivia} $$

Answer:

Emma > Sally > Olivia