Question

determine the quartiles, the iqr, and then use the 1.5 x iqr rule to check for outliers. q1 = q3 = iqr = a data value must be lower than to be considered a low outlier (the lower limit). a data value must be higher than to be considered a high outlier (the upper limit). list any data values flagged as outliers. list your answers, separated with commas.

Explanation:

Step1: Arrange data in ascending - order

Assume the data values from the bar - graph are: 40, 60, 80, 100, 120, 140, 160.
The number of data points $n = 7$.
The first quartile $Q_1$ position: $Q_1$ position $=\frac{n + 1}{4}=\frac{7+1}{4}=2$. So $Q_1$ is the 2nd value in the ordered data set, $Q_1 = 60$.

Step2: Calculate the third quartile $Q_3$

$Q_3$ position $=\frac{3(n + 1)}{4}=\frac{3\times(7 + 1)}{4}=6$. So $Q_3$ is the 6th value in the ordered data set, $Q_3 = 140$.

Step3: Calculate the inter - quartile range (IQR)

$IQR=Q_3 - Q_1=140 - 60 = 80$.

Step4: Find the lower and upper bounds for outliers

Lower bound for outliers $=Q_1-1.5\times IQR=60-1.5\times80=60 - 120=- 60$.
Upper bound for outliers $=Q_3 + 1.5\times IQR=140+1.5\times80=140 + 120 = 260$.
Since all the data values (40, 60, 80, 100, 120, 140, 160) are within the range $[-60,260]$, there are no outliers.

Answer:

$Q_1 = 60$
$Q_3 = 140$
$IQR = 80$
No outliers.