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 third quartile (q3) is less than $23.00. the median expense is greater than $25.00. the first quartile (q1) is $21.25.

Explanation:

Step1: Arrange data in ascending order

$19.50, 21.75, 22.00, 22.25, 22.75, 23.50, 26.75$

Step2: Find the minimum and maximum

Min = $19.50$, Max = $26.75$

Step3: Calculate the range

Range = Max - Min = $26.75 - 19.50=7.25$

Step4: Find the median (Q2)

Since $n = 7$ (odd), median is the 4 - th value. So Q2=$22.25$

Step5: Find the first quartile (Q1)

The lower half of data is $19.50, 21.75, 22.00$. Since $n = 3$ (odd), Q1 is the 2 - nd value, so Q1 = $21.75$

Step6: Find the third quartile (Q3)

The upper half of data is $22.75, 23.50, 26.75$. Since $n = 3$ (odd), Q3 is the 2 - nd value, so Q3 = $23.50$

Answer:

The range of expenses is $7.25>7.00$, Q3 = $23.50>23.00$, median = $22.25<25.00$, Q1 = $21.75
eq21.25$. The correct statement is that the range of expenses is greater than $\$7.00$. But among the given options, the closest correct - like analysis shows that the range of expenses is $\$7.25$ which means the statement "The range of expenses is $\$7.00$" is false, the third quartile Q3 = $23.50>23.00$, the median $22.25<25.00$ and Q1 = $21.75
eq21.25$. There seems to be an error in the options provided as none are exactly correct based on our calculations, but if we consider the range calculation, the range ($7.25$) is close to the statement about the range being $\$7.00$ in a sense of comparison. If we assume a rounding - off or approximation context in the options, the range of expenses calculation shows that the range is greater than $\$7.00$. So, if we have to pick from the given options, the statement "The range of expenses is $\$7.00$" is false which implies that the range is actually greater than $\$7.00$ (since our calculated range is $7.25$). So the answer is that the range of expenses is greater than $\$7.00$ (even though it's not an exact match in the options as written, it's the most reasonable conclusion based on the data).