Question

6. Here are 10 test scores: 50, 74, 76, 77, 78, 79, 80, 80, 82, 84. The mean of these scores is 76. How does removing the outlier 50 affect the mean? * A. The set has 50 as an outlier and removing it decreases the mean by about 2. B. The set has 50 as an outlier and removing it increases the mean by about 3. C. The set has 50 as an outlier and removing it decreases the mean by about 6.

Answer 1

Answer is Choice B) removing 50 as the outlier increases the mean by about 3

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Explanation:

Add up the ten values to get: 50+74+76+77+78+79+80+80+82+84 = 760

Divide that result by 10 because there are 10 test scores: 760/10 = 76

That's how they got the mean to be 76. This process (of adding the values and dividing by the number of values) is going to be repeated. However, we'll take out 50

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So the new list is now: {74, 76, 77, 78, 79, 80, 80, 82, 84}

Add up those values: 74+76+77+78+79+80+80+82+84 = 710

Divide by 9: 710/9 = 78.889 (approximate)

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The old mean was 76. The new mean is now 78.889 approximately. The increase is due to the fact that we removed the left-most outlier. The outlier on the left pulls the mean down to be smaller than it should be. 

Jumping from 76 to 78.889 is an increase of 2.889. We can see this through subtraction: 78.889 - 76 = 2.889. This value rounds to 3. So there's an increase of about 3.