you work for a large farm with many fields of corn. you gather the following data: mass(g) of ears of corn…

you work for a large farm with many fields of corn. you gather the following data: mass(g) of ears of corn 512.2 516.2 575.8 530.3 710 706.2 490.6 636.5 448.8 857.8 451.4 585.9 518.3 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) iqr b) apply the 1.5 iqr rule to search for outliers. report the lower and upper cutoffs. lower: upper: are there any low outliers by the 1.5 x iqr rule? (yes or no) are there any high outliers by the 1.5 x iqr rule? (yes or no)

you work for a large farm with many fields of corn. you gather the following data: mass(g) of ears of corn 512.2 516.2 575.8 530.3 710 706.2 490.6 636.5 448.8 857.8 451.4 585.9 518.3 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) iqr b) apply the 1.5 iqr rule to search for outliers. report the lower and upper cutoffs. lower: upper: are there any low outliers by the 1.5 x iqr rule? (yes or no) are there any high outliers by the 1.5 x iqr rule? (yes or no)

Answer

Explanation:

Step1: Arrange data in ascending order

448.8, 451.4, 490.6, 512.2, 516.2, 518.3, 530.3, 575.8, 636.5, 706.2, 710, 857.8

Step2: Find the median (Q2)

There are 12 data - points. The median is the average of the 6th and 7th ordered values. So, $Q2=\frac{518.3 + 530.3}{2}=524.3$

Step3: Find Q1 and Q3

The lower half of the data is 448.8, 451.4, 490.6, 512.2, 516.2, 518.3. The median of the lower half (Q1) is $\frac{490.6+512.2}{2}=501.4$. The upper half of the data is 530.3, 575.8, 636.5, 706.2, 710, 857.8. The median of the upper half (Q3) is $\frac{636.5 + 706.2}{2}=671.35$

Step4: Calculate IQR

$IQR = Q3 - Q1=671.35−501.4 = 169.95$

Step5: Calculate lower and upper cut - offs for outliers

Lower cut - off: $Q1-1.5\times IQR=501.4−1.5\times169.95=501.4 - 254.925 = 246.475$ Upper cut - off: $Q3 + 1.5\times IQR=671.35+1.5\times169.95=671.35 + 254.925 = 926.275$

Step6: Check for low outliers

Since all the data - points are greater than 246.475, there are no low outliers.

Step7: Check for high outliers

Since all the data - points are less than 926.275, there are no high outliers.

Answer:

a) IQR: 169.95 b) Lower: 246.475 Upper: 926.275 Are there any low outliers (yes or no): no Are there any high outliers (yes or no): no