Question

which of the following points, if added to the table, would be an outlier?

(7, 73)
(7.5, 70)
(8, 35)
(8.5, 66)

Explanation:

Analyze the trend of the existing data points

The given data points \((x, y)\) are:

• \((6, 71)\)
• \((7, 68)\)
• \((7.5, 69)\)
• \((7.5, 65)\)
• \((8, 63)\)
• \((8.25, 62)\)
• \((8.25, 64)\)
• \((9, 60)\)
• \((9.5, 61)\)

As \(x\) increases from \(6\) to \(9.5\), \(y\) generally decreases from around \(71\) to \(61\). This indicates a strong negative linear association where \(y\) values stay within the range of \([60, 71]\).

Evaluate the given options against the trend

• \((7, 73)\): For \(x = 7\), \(y = 73\) is very close to the existing point \((6, 71)\) and follows the general downward trend.
• \((7.5, 70)\): For \(x = 7.5\), \(y = 70\) is extremely close to the existing points \((7, 68)\) and \((7.5, 69)\).
• \((8, 35)\): For \(x = 8\), the expected \(y\) value based on the trend is around \(63\). A \(y\) value of \(35\) is extremely far below the rest of the data.
• \((8.5, 66)\): For \(x = 8.5\), \(y = 66\) fits well within the cluster of points around \(x = 8\) to \(9\).

Identify the outlier

The point \((8, 35)\) deviates drastically from the established negative linear pattern of the dataset, making it a clear outlier.

Answer:

• (A) \((7, 73)\)
• (B) \((7.5, 70)\)
• (C) \((8, 35)\) (Correct answer)
• (D) \((8.5, 66)\)