Question

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 6.

B.
The set has 50 as an outlier and removing it decreases the mean by about 2.

C.
The set has 50 as an outlier and removing it increases the mean by about 3.

Answer 1

The answer is C. 
The set has 50 as an outlier and removing it increases the mean by about 3.

Since 50 is significantly smaller number than all others, it is expected that removing 50 will increase the mean.
The first mean is 76:
$X_{1} = \frac{50+74+76+77+78+79+80+80+82+84}{10} = \frac{760}{10} =76$

The mean after removing 50 is:
$X_{2} = \frac{74+76+77+78+79+80+80+82+84}{10} = \frac{710}{90} =78.89$
X₂ ≈ 79

The difference between the second and the first mean is 79 - 76 = 3, thus 
removing 50 as an outlier increases the mean by about 3.