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. 32 12 36 9 40 27 29 32 35 10 send data to excel part: 0 / 3 part 1 of 3 first quartile $q_1$ is

Explanation:

Step1: Sort the data

$9, 10, 12, 27, 29, 32, 32, 35, 36, 40$

Step2: Find the position of $Q_1$

The formula for the position of the first - quartile $Q_1$ for a sample of size $n$ is $i=\frac{1}{4}(n + 1)$. Here $n = 10$, so $i=\frac{1}{4}(10 + 1)=2.75$.

Step3: Calculate $Q_1$

Since $i$ is not an integer, $Q_1$ is the value that is $0.75$ of the way between the 2nd and 3rd ordered data values. The 2nd value is $10$ and the 3rd value is $12$. So $Q_1=10+(12 - 10)\times0.75=10 + 1.5=11.5$.

Step4: Find the position of $Q_3$

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

Step5: Calculate $Q_3$

Since $i$ is not an integer, $Q_3$ is the value that is $0.25$ of the way between the 8th and 9th ordered data values. The 8th value is $35$ and the 9th value is $36$. So $Q_3=35+(36 - 35)\times0.25=35.25$.

Step6: Calculate the IQR

The inter - quartile range $IQR = Q_3-Q_1$. So $IQR=35.25-11.5 = 23.75$.

Answer:

First quartile $Q_1$ is $11.5$, third quartile $Q_3$ is $35.25$, and $IQR$ is $23.75$.