Question

you work for a large farm with many fields of corn. you are investigating the mass of a sample of ears of corn. you gather the following data: mass(g) of ears of corn 613.5 637.2 561.4 671.8 628.3 527.5 455.4 567 766.6 372.1 488.4 387 676.6 checksum: 7352.8 some of the masses in the sample seem much larger than the rest. you decide to make several calculations describing the \spread\ of the data set. you hope to use them to help in the search for outliers. find the following: a) q1 b) q3 c) iqr d) apply the 1.5 iqr rule to search for outliers. report the lower and upper fences. lower: upper: are there any outliers by the 1.5 iqr rule? (enter \yes\ or
o\)

Explanation:

Step1: Sort the data

$372.1,387,455.4,488.4,527.5,561.4,567,613.5,628.3,637.2,671.8,676.6,766.6$

Step2: Find the position of Q1

There are $n = 13$ data - points. The position of Q1 is $i=\frac{n + 1}{4}=\frac{13+1}{4}=3.5$. So, $Q1=\frac{455.4 + 488.4}{2}=471.9$

Step3: Find the position of Q3

The position of Q3 is $i = \frac{3(n + 1)}{4}=\frac{3\times(13 + 1)}{4}=10.5$. So, $Q3=\frac{637.2+671.8}{2}=654.5$

Step4: Calculate the IQR

$IQR=Q3 - Q1=654.5-471.9 = 182.6$

Step5: Calculate the lower and upper fences

Lower fence $=Q1-1.5\times IQR=471.9-1.5\times182.6=471.9 - 273.9=198$
Upper fence $=Q3 + 1.5\times IQR=654.5+1.5\times182.6=654.5+273.9 = 928.4$

Step6: Check for outliers

Since all the data - points are within the range of $198$ and $928.4$, there are no outliers.

Answer:

a) $471.9$
b) $654.5$
c) $182.6$
d) Lower: $198$, Upper: $928.4$, Are there any outliers by the 1.5 IQR rule? no