Answer :
The data set contains no outliers since all of the values are within the bounds of 148.5 and 198.5.
The following is the five-number summary of the given data set 68, 162, 163, 167, 167, 168, 168, 169, 170, 178, 180, 180, 182, 182, 185. Identify any outliers.
The five-number summary of the data set are as follows:Minimum value = 68 First quartile = 167Median = 169Third quartile = 180Maximum value = 185 We use the following formula to find outliers in the data set:IQR = Q3 - Q1 Here, Q1 and Q3 are the first and third quartiles, respectively.So,IQR = 180 - 167IQR = 13 To find the lower and upper bounds, we use the following formulas:Lower bound = Q1 - (1.5 × IQR)Upper bound = Q3 + (1.5 × IQR)Here, the lower bound and upper bound values are calculated as follows:Lower bound = 167 - (1.5 × 13)Lower bound = 148.5Upper bound = 180 + (1.5 × 13)Upper bound = 198.5
Now, any values that are less than the lower bound or greater than the upper bound are considered outliers.The data set contains no outliers since all of the values are within the bounds of 148.5 and 198.5.
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