Question

ears of corn. you gather the following data: mass(g) 455.1 585.6 601.8 545.5 519.8 756.5 494.7 677.8 464.6 471.8 634 470 507.6 some of the masses in the sample seem much larger than the rest. you decide to make several calculations to help in the search for outliers. report your answer with all the decimal places. find the following: a. the 26th percentile = 471.8 b. iqr = c. apply the 1.5 iqr rule to search for outliers. report the lower and upper cutoffs limits (fences). lower: upper:

Explanation:

Step1: Sort the data

First, sort the data in ascending - order: 455.1, 464.6, 470, 471.8, 494.7, 507.6, 519.8, 545.5, 585.6, 601.8, 634, 677.8, 756.5

Step2: Calculate the first quartile ($Q_1$)

The position of the first quartile for $n = 13$ data - points is $i=\frac{1}{4}(n + 1)=\frac{1}{4}(13 + 1)=3.5$. So, $Q_1=470+(471.8 - 470)\times0.5 = 470.9$.

Step3: Calculate the third quartile ($Q_3$)

The position of the third quartile is $i=\frac{3}{4}(n + 1)=\frac{3}{4}(13 + 1)=10.5$. So, $Q_3=601.8+(634 - 601.8)\times0.5=617.9$.

Step4: Calculate the IQR

The inter - quartile range (IQR) is $IQR=Q_3 - Q_1=617.9 - 470.9 = 147$.

Step5: Calculate the lower and upper cutoffs

The lower cutoff is $Q_1-1.5\times IQR=470.9-1.5\times147=470.9 - 220.5 = 250.4$.
The upper cutoff is $Q_3 + 1.5\times IQR=617.9+1.5\times147=617.9 + 220.5 = 838.4$.

Answer:

b. IQR = 147
c. Lower: 250.4
Upper: 838.4