To identify an outlier in the dataset {176, 152, 18, 176, 136, 184, 181, 176}, we can use the interquartile range (IQR) method or simply look for values that are significantly different from the others.
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Calculate the quartiles:
- The sorted dataset is: {18, 136, 152, 176, 176, 176, 181, 184}.
- The median (Q2) is the average of the two middle values (176 and 176), which is 176.
- The first quartile (Q1) is the median of the first half of the data (18, 136, 152) which is 136.
- The third quartile (Q3) is the median of the second half of the data (176, 176, 181, 184) which is 178.5.
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Calculate the IQR:
- IQR = Q3 - Q1 = 178.5 - 136 = 42.5.
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Determine the outlier bounds:
- Lower bound = Q1 - 1.5 * IQR = 136 - 1.5 * 42.5 = 136 - 63.75 = 72.25.
- Upper bound = Q3 + 1.5 * IQR = 178.5 + 1.5 * 42.5 = 178.5 + 63.75 = 242.25.
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Identify outliers: Any value below 72.25 or above 242.25 is considered an outlier. In this dataset, the only value that falls below 72.25 is 18.
Thus, the outlier in the dataset is 18.