Question

Part 1 of 4Suppose the data represent the inches rainfall in April for a certain city over the course of 20 yearsGiven the quartiles Q1= 1.970, Q=3.380, and Q3 = 4.770, determine the lower and upper fences. Are there any outliers, according to this criterion?0.330.771.251.541.822.122.452.883.053.233.533.844.064.534.684.865.225.435.816.27

Answer 1

For this problem, we were given a certain dataset, as well as the quartiles Q1, Q, and Q3. From this information, we need to determine the lower and upper fences.

The fences are given by:

`\begin{gathered} \text{lower}=Q_1-(1.5)\cdot\text{IQR} \\ \text{upper}=Q_3+(1.5)\cdot\text{IQR} \end{gathered}`

Therefore, we need to calculate the value of the IQR, which is the subtraction between Q3 and Q1.

`\begin{gathered} \text{IQR}=Q_3-Q_1=4.77-1.97 \\ \text{IQR}=2.8 \end{gathered}`

With this, we have all the data to determine the lower and upper fences. The calculations are shown below:

`\begin{gathered} \text{lower}=1.97-(1.5)\cdot2.8 \\ \text{lower}=-2.23 \\ \text{upper}=4.77+\cdot(1.5)\cdot2.8 \\ \text{upper}=8.97 \end{gathered}`

Since there aren't any values that are lower than the lower fence or higher than the upper fence, we don't have any outlier on this data.