Question

you work for a large farm with many fields of corn. you are investigating the mass in grams of a sample of ears of corn. you gather the following data: mass(g) 481.1 689.6 497 556.6 574.9 479.7 531.4 824.7 510.8 422.7 416.6 488.6 652.2 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 34th percentile = 484.2× b. iqr = 90.27× c. apply the 1.5 iqr rule to search for outliers. report the lower and upper cutoffs limits (fences). lower: 344.6× upper: 705.7×

Explanation:

Step1: Arrange data in ascending order

416.6, 422.7, 479.7, 481.1, 488.6, 497, 510.8, 531.4, 556.6, 574.9, 652.2, 689.6, 824.7

Step2: Calculate 34th percentile

$n = 13$ (number of data - points). Index $i=0.34\times n=0.34\times13 = 4.42$. The 34th - percentile is $481.1+(488.6 - 481.1)\times(4.42 - 4)=481.1+7.5\times0.42 = 481.1 + 3.15=484.25$

Step3: Find first and third quartiles

The median (second - quartile $Q_2$) of the 13 - data set is the 7th value, so $Q_2 = 510.8$. The first quartile $Q_1$ is the median of the first 6 values. Since $n_1 = 6$ (even), $Q_1=\frac{481.1 + 488.6}{2}=484.85$. The third quartile $Q_3$ is the median of the last 6 values. Since $n_2 = 6$ (even), $Q_3=\frac{574.9+652.2}{2}=613.55$.

Step4: Calculate IQR

$IQR=Q_3 - Q_1=613.55 - 484.85 = 128.7$

Step5: Calculate lower and upper cut - offs

Lower cut - off $=Q_1-1.5\times IQR=484.85-1.5\times128.7=484.85 - 193.05=291.8$
Upper cut - off $=Q_3 + 1.5\times IQR=613.55+1.5\times128.7=613.55 + 193.05=806.6$

Answer:

a. 484.25
b. 128.7
c. Lower: 291.8, Upper: 806.6