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QuestionMathematics
What is the outlier in the following set?
29, 2, 28, 30, 26, 31
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Answer
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Step 1:: Identify the data set.
The given data set is {29, 2, 28, 30, 26, 31}.
Step 2:: Understand the concept of an outlier.
An outlier is a data point that significantly differs from other data points in the data set. There are several methods to detect outliers, such as the IQR method, Z-score method, and the modified Z-score method. In this case, we will use the IQR method.
Step 3:: Calculate the first quartile (Q1), the median (Q2), and the third quartile (Q3).
- Sort the data set in ascending order: {2, 26, 28, 29, 30, 31} - Calculate the median (Q2): (28 + 29) / 2 = 28.5 - Since there are 6 data points, Q^1 is the average of the 3rd and 4th data points, and Q^3 is the average of the 4th and 5th data points: - Q^1 = (26 + 28) / 2 = 27 - Q^3 = (29 + 30) / 2 = 29.5
Step 4:: Calculate the interquartile range (IQR).
IQR = Q^3 - Q^1 = 29.5 - 27 = 2.5
Step 5:: Determine the lower outlier boundary and the upper outlier boundary.
- Lower outlier boundary: Q^1 - 1.5 * IQR = 27 - 1.5 * 2.5 = 24.75 - Upper outlier boundary: Q^3 + 1.5 * IQR = 29.5 + 1.5 * 2.5 = 34.25
Step 6:: Identify the outlier(s).
- Check if any data point is below the lower outlier boundary or above the upper outlier boundary: - The data point 2 is below the lower outlier boundary (24.75), so it is an outlier.
Final Answer
The outlier in the given data set is 2.
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