Question

bowen recorded his daily expenses for a week as follows: $21.75, $22.75, $22.25, $19.50, $23.50, $22.00 and $26.75. which statement about the box - plot representing bowens daily expenses is true? the range of expenses is $7.00. the median expense is greater than $25.00. the third quartile (q3) is less than $23.00. the first quartile (q1) is $21.25.

Explanation:

Step1: Recall box - plot properties

In a box - plot, the box represents the inter - quartile range (IQR) with the left edge as Q1, the middle line as Q2 (median), and the right edge as Q3. The minimum value is at the end of the left whisker and the maximum value is at the end of the right whisker.

Step2: Analyze the given box - plot

From the box - plot, we can see that:

• The minimum (Min) is around $19$.
• The first quartile (Q1) is approximately $21$.
• The median (Q2) is around $22$.
• The third quartile (Q3) is approximately $23$.
• The maximum (Max) is around $26$.

Step3: Check each statement

• For the range, Range = Max - Min. Here, Max=$26$ and Min = $19$, so Range=$26 - 19=7$.
• The median (Q2) is around $22$, which is less than $25$.
• The third quartile (Q3) is approximately $23$.
• The first quartile (Q1) is approximately $21$.

Answer:

The statement "The range of expenses is $7.00$" is true.