Question

medical marijuana 2015 sales tax: the data show the amount of sales tax paid in a county in colorado. find the first and third quartiles for the data.
month \tsales tax \tmonth \tsales tax
january \t363,946 \tjuly \t518,706
february \t358,807 \taugust \t554,113
march \t418,590 \tseptember \t506,979
april \t266,266 \toctober \t341,851
may \t399,810 \tnovember \t349,848
june \t453,062 \tdecember \t532,061
send data to excel
your answer
part 1 of 2
first quartile ( q_1 ) is \boxed{361,376.5} (with red error)
correct answer
first quartile ( q_1 ) is 354,327.5.
part: 1 / 2
part 2 of 2
third quartile ( q_3 ) is (square).

Explanation:

Step1: List the data in order

First, we list all the sales tax values in ascending order: 266,266; 341,851; 349,848; 358,807; 363,946; 399,810; 418,590; 453,062; 506,979; 518,706; 532,061; 554,113. There are 12 data points.

Step2: Find the position of \( Q_3 \)

The formula for the position of the third quartile (\( Q_3 \)) is \( \frac{3(n + 1)}{4} \), where \( n = 12 \). So \( \frac{3(12 + 1)}{4}=\frac{3\times13}{4}=9.75 \).

Step3: Calculate \( Q_3 \)

This means \( Q_3 \) is 0.75 of the way between the 9th and 10th values. The 9th value is 506,979 and the 10th value is 518,706. We use the formula \( Q_3 = \text{9th value}+ 0.75\times(\text{10th value}-\text{9th value}) \).
Substitute the values: \( 506,979+0.75\times(518,706 - 506,979) \)
First, calculate the difference: \( 518,706 - 506,979 = 11,727 \)
Then, calculate \( 0.75\times11,727 = 8,795.25 \)
Finally, add to the 9th value: \( 506,979+8,795.25 = 509,842.5 \)

Answer:

509,842.5