Question

taxes the data for a recent year show the taxes (in millions of dollars) received from a random sample of 10 states. find the first and third quartiles and the iqr. 40 24 17 36 6 6 38 16 35 17 send data to excel part: 0 / 3 part 1 of 3 first quartile $q_1$ is

Explanation:

Step1: Sort the data

$-6,6,16,17,17,24,35,36,38,40$

Step2: Find the position of $Q_1$

The formula for the position of $Q_1$ is $i=\frac{n + 1}{4}$, where $n = 10$. So $i=\frac{10+ 1}{4}=2.75$.

Step3: Calculate $Q_1$

Since $i$ is not an integer, we interpolate. $Q_1$ is the value at the 2 - nd position plus $0.75$ times the difference between the values at the 3 - rd and 2 - nd positions. The 2 - nd value is $6$ and the 3 - rd value is $16$. So $Q_1=6+(16 - 6)\times0.75=6 + 7.5=13.5$.

Step4: Find the position of $Q_3$

The formula for the position of $Q_3$ is $i=\frac{3(n + 1)}{4}$, so $i=\frac{3\times(10 + 1)}{4}=8.25$.

Step5: Calculate $Q_3$

Since $i$ is not an integer, we interpolate. $Q_3$ is the value at the 8 - th position plus $0.25$ times the difference between the values at the 9 - th and 8 - th positions. The 8 - th value is $36$ and the 9 - th value is $38$. So $Q_3=36+(38 - 36)\times0.25=36+0.5 = 36.5$.

Step6: Calculate the IQR

The inter - quartile range $IQR=Q_3 - Q_1$. So $IQR=36.5-13.5 = 23$.

Answer:

First quartile $Q_1$ is $13.5$, Third quartile $Q_3$ is $36.5$, IQR is $23$