Answer:
Third choice
Explanation:
Let's see, let's write the numbers in order.
-6,-2,1,1,4,4,14
So we can see that yes, indeed, it could be either -6 or 14.
We can also rule out the first choice and the last choice, because they lack in common sense. -6, being lesser, would not raise the mean, it would lower it. 14, being the greatest, would not lower the mean, it would raise it.
Now let's put our numbers through trial. Find the mean of the whole set.
-6+-2+1+1+4+4+14 = 16
16/7
16/7 is approximately 2.3. We round to the nearest tenth because the numbers in the answers (1.9) are rounded to the nearest tenth.
Now we will exclude 14 to see how much it changes.
-6+-2+1+1+4+4 = 2
2/6 = 1/3
1/3 is approximately 0.3. We can see that the mean has decreased by around 2 just from removing the 14.
Now let's exclude -6 and see how much it changes.
-2+1+1+4+4+14 = 22
22/6 is approximately 3.7. We can see that the mean has increased by around 1.4.
Both the second and the third choice are plausible, but we are looking for the outlier, meaning the one that is further away from the rest of the numbers. The mean decreased by around 2 (which is near 1.9) when 14 is removed, which is greater than 1.4 (or 1), so we can assume that the third choice is the answer.
We can also back this up by finding how much each number is close to the mean. -6 is closer to 2.3 than 14, because if you add 6 to 2.3 (to get the distance between them), it is 8.3, while if you subtract 14 by 2.3, you get 11.7, which is greater than 8.3
Another way to double check this is to see how far away the numbers are from the rest of the numbers. This is not a very accurate way, but it can be useful in double checking. -6 and -2 are only 4 units apart, while 4 and 14 are 10 units apart. 10>4, naturally.