Find the outlier in the data set and tell how it affects the mean.
4, 4, –6, –2, 14, 1, 1
• –6; it raises the mean by about 1.
• –6; it lowers the mean by about 1.
• 14; it raises the mean by about 1.9.
• 14; it lowers the mean by about 1.9.
14; it raises the mean by about 1.9.
To find the outlier in the given data set and determine how it affects the mean, we need to calculate the mean with and without each value, and compare how much it changes the mean.
Let's calculate the mean without the values –6 and 14:
Mean without –6:
(4 + 4 – 2 + 14 + 1 + 1) / 6 = 22 / 6 = 3.67
Mean without 14:
(4 + 4 – 6 – 2 + 1 + 1) / 6 = 2 / 6 = 0.33
Now we can compare the mean with the original mean of the data set, which is (4 + 4 – 6 – 2 + 14 + 1 + 1) / 7 = 16 / 7 = 2.29:
• –6 affects the mean by (2.29 - 3.67) ≈ -1.38. It lowers the mean by about 1.38.
• 14 affects the mean by (2.29 - 0.33) ≈ 1.96. It raises the mean by about 1.96.
Therefore, the correct answer is: 14; it raises the mean by about 1.9.