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Which option is true about the outliers of the skewed dataset 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16?(1 point) Responses The outliers of the dataset are 5, 14, and 16. The outliers of the dataset are 5, 14, and 16. There are no outliers in the dataset. There are no outliers in the dataset. The outliers of the dataset are 14 and 16. The outliers of the dataset are 14 and 16. The only outlier of the dataset is 16.

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To determine the outliers in the skewed dataset (5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16), we can use the interquartile range (IQR) method, which is commonly used to identify outliers.

  1. Find the quartiles:

    • The median (Q2) is the average of the 6th and 7th values in the ordered list: (8 + 9) / 2 = 8.5.
    • The first quartile (Q1) is the median of the first half of the data: (6 + 7) / 2 = 6.5.
    • The third quartile (Q3) is the median of the second half of the data: (9 + 14) / 2 = 11.5.

  2. Calculate the IQR:

    • IQR = Q3 - Q1 = 11.5 - 6.5 = 5.

  3. Determine the lower and upper bounds for outliers:

    • Lower Bound = Q1 - 1.5 * IQR = 6.5 - 1.5 * 5 = 6.5 - 7.5 = -1.
    • Upper Bound = Q3 + 1.5 * IQR = 11.5 + 1.5 * 5 = 11.5 + 7.5 = 19.

  4. Identify outliers:

    • Any value below -1 or above 19 is considered an outlier. In this dataset, the only values that are outliers are 14 and 16, since they are above 19.

Based on this analysis, the correct response is: The outliers of the dataset are 14 and 16.