Questions: e) Using rule #1, are there any outliers in the Southside's distribution? Show your work. IQR = 652.5 - 422.5 = 230 LB = 422.5 - 1.5(230) UB = 652.5 + 1.5(230) Using rule #2, are there any outliers in the Southside's distribution? Show your work. Means = 517.22 f) Remove the value of 285 mg from the Southside cholesterol's data set. Use your calculator to find the following values again: Mean Min Q1 Med Q3 Max Std. Dev --------------------------------------- Southside What values changed the most? What values changed the least? 2) When drilling for oil wells, researchers have to take into account how much oil each well will eventually produce before deciding if they should drill in a specific location. In the table below, there are the total amounts of oil recovered from 38 wells in the Michigan basin, in thousands of barrels. 3 31 38 50 65 92 ----------------------- 13 33 43 50 66 98 15 35 43 53 70 157 19 35 45 56 70 21 35 46 57 74 22 37 48 59 80 25 37 49 63 82 a) What measures would you use to describe the center and spread of these data? Justify your answer.

e) Using rule #1, are there any outliers in the Southside's distribution? Show your work. IQR = 652.5 - 422.5 = 230 LB = 422.5 - 1.5(230) UB = 652.5 + 1.5(230) Using rule #2, are there any outliers in the Southside's distribution? Show your work. Means = 517.22 f) Remove the value of 285 mg from the Southside cholesterol's data set. Use your calculator to find the following values again: Mean Min Q1 Med Q3 Max Std. Dev --------------------------------------- Southside What values changed the most? What values changed the least? 2) When drilling for oil wells, researchers have to take into account how much oil each well will eventually produce before deciding if they should drill in a specific location. In the table below, there are the total amounts of oil recovered from 38 wells in the Michigan basin, in thousands of barrels. 3 31 38 50 65 92 ----------------------- 13 33 43 50 66 98 15 35 43 53 70 157 19 35 45 56 70 21 35 46 57 74 22 37 48 59 80 25 37 49 63 82 a) What measures would you use to describe the center and spread of these data? Justify your answer.
Transcript text: e) Using rule \#1, are there any outliers in the Southside's distribution? Show your work. \[ \begin{array}{l} I Q R=652.5-422.5=230 \\ L B=422.5-1.5(230)= \\ U B=652.5+1.5(230)= \end{array} \] Using rule \#2, are there any outliers in the Southside's distribution? Show your work. \[ \text { Mrans }=517.22 \] f) Remove the value of 285 mg from the Southside cholesterol's data set. Use your calculator to find the following values again: \begin{tabular}{|l|l|l|l|l|l|l|l|} \hline & Mean & Min & Q1 & Med & Q3 & Max & Std. Dev \\ \hline Southside & & & & & & & \\ \hline \end{tabular} What values changed the most? What values changed the least? 2) When drilling for oil wells, researchers have to take into account how much oil each well will eventually produce before deciding if they should drill in a specific location. In the table below, there are the total amounts of oil recovered from 38 wells in the Michigan basin, in thousands of barrels. \begin{tabular}{|l|l|l|l|l|l|} \hline 3 & 31 & 38 & 50 & 65 & 92 \\ \hline 13 & 33 & 43 & 50 & 66 & 98 \\ \hline 15 & 35 & 43 & 53 & 70 & 157 \\ \hline 19 & 35 & 45 & 56 & 70 & \\ \hline 21 & 35 & 46 & 57 & 74 & \\ \hline 22 & 37 & 48 & 59 & 80 & \\ \hline 25 & 37 & 49 & 63 & 82 & \\ \hline \end{tabular} a) What measures would you use to describe the center and spread of these data? Justify your answer.
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Solution

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Solution Steps

Step 1: Identify the Interquartile Range (IQR)

To determine if there are any outliers in the Southside's distribution using rule #1, we first need to calculate the Interquartile Range (IQR). The IQR is found by subtracting the first quartile (Q1) from the third quartile (Q3).

Given:

  • Q1 = 492.5
  • Q3 = 652.5

\[ \text{IQR} = Q3 - Q1 = 652.5 - 492.5 = 160 \]

Step 2: Calculate the Lower and Upper Bounds

Using the IQR, we can calculate the lower and upper bounds to identify outliers. The lower bound (LB) is calculated as Q1 - 1.5 * IQR, and the upper bound (UB) is calculated as Q3 + 1.5 * IQR.

\[ \text{LB} = Q1 - 1.5 \times \text{IQR} = 492.5 - 1.5 \times 160 = 492.5 - 240 = 252.5 \] \[ \text{UB} = Q3 + 1.5 \times \text{IQR} = 652.5 + 1.5 \times 160 = 652.5 + 240 = 892.5 \]

Step 3: Determine Outliers Using Rule #1

Any value below the lower bound or above the upper bound is considered an outlier.

  • Lower Bound: 252.5
  • Upper Bound: 892.5

Check the data set to see if any values fall outside these bounds. If there are values less than 252.5 or greater than 892.5, they are outliers.

Final Answer

Using rule #1, any values in the Southside's distribution that are less than 252.5 or greater than 892.5 are considered outliers.

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