Question

The following 10 scores were input in the gradebook for Prof. Williams's class. 73, 74, 75, 75, 76, 77, 81, 83, 86, 88 Identify all values that are outliers. If there is more than one outlier, separate them with commas. If there are no outliers, click on "None".

Answer 1

To identify any outliers in the given set of scores, we can use the concept of outliers based on the interquartile range (IQR).

First, we need to find the IQR, which is the range between the first quartile (Q1) and the third quartile (Q3).

Given scores: 73, 74, 75, 75, 76, 77, 81, 83, 86, 88

Step 1: Arrange the scores in ascending order:

73, 74, 75, 75, 76, 77, 81, 83, 86, 88

Step 2: Calculate Q1 and Q3:

Q1 = 75 (the median of the lower half of the scores)

Q3 = 83 (the median of the upper half of the scores)

Step 3: Calculate the IQR:

IQR = Q3 - Q1

IQR = 83 - 75

IQR = 8

Now, to identify outliers, we can use the following rule:

- Any value less than Q1 - 1.5 * IQR or greater than Q3 + 1.5 * IQR is considered an outlier.

Calculating the lower and upper bounds:

Lower bound = Q1 - 1.5 * IQR

Lower bound = 75 - 1.5 * 8

Lower bound = 75 - 12

Lower bound = 63

Upper bound = Q3 + 1.5 * IQR

Upper bound = 83 + 1.5 * 8

Upper bound = 83 + 12

Upper bound = 95

Now, let's check which values fall outside the lower and upper bounds:

73 (outlier - below lower bound)

74 (outlier - below lower bound)

75

75

76

77

81

83

86

88

Based on the calculations, the values 73 and 74 are outliers as they fall below the lower bound. Therefore, the outliers in the given set of scores are 73, 74.

Explanation:

No step by step explaination