Mean - conceptual explanation

1. The Mean
Conceptual Explanation

2. Mean
Here is a technical definition of the “mean”:

3. Mean
Here is a technical definition of the “mean”:
“The mean represents the balance point of the
distribution and takes into account the weighted
value of each observation”.

4. Let’s break this definition down:

5. Let’s break this definition down:
“The mean represents the balance point of the
distribution and takes into account the weighted
value of each observation”.

6. Let’s break this definition down:
“The mean represents the balance point of the
distribution and takes into account the
weighted value of each observation”.

7. Let’s break this definition down:
“The mean represents the balance point of the
distribution and takes into account the
weighted value of each observation”.
Imagine a teeter-totter

8. Let’s break this definition down:
“The mean represents the balance point of the
distribution and takes into account the
weighted value of each observation”.
3

9. Let’s break this definition down:
“The mean represents the balance point of the
distribution and takes into account the
weighted value of each observation”.
With one observation the balance point (or
fulcrum) is wherever that observation is. In this
case 3.
3

10. Let’s break this definition down:
“The mean represents the balance point of the
distribution and takes into account the
weighted value of each observation”.
With one observation the balance point (or
fulcrum) is wherever that observation is. In this
case 3.
3
3

11. If we add a 5,
3 5

12. If we add a 5, then we have a new balance point
to keep both sides equal.

13. If we add a 5, then we need a new balance point
to keep both sides equal.
then we have a new balance point to keep both
sides equal.

14. If we add a 5, then we have a new balance point
to keep both sides equal.
3 5

15. If we add a 5, then we have a new balance point
to keep both sides equal.
3 5
4

16. Let’s add a 4
3 5
4

17. Let’s add a 4
3 5
4
4

18. Let’s add a 4, and the balance point remains 4
3 5
4
4

19. Let’s add a 4, and the balance point remains 4,
because everything is still balanced.
3 5
4
4

20. Let’s add an “8”,
3 5
4
4

21. Let’s add an “8”,
3 5
4
4 8

22. Let’s add an “8”,
5
4
4
8
3

23. Let’s add an “8”, and the new balance point will
be 5 . . . so that everything stays equal.
5
4
4
8
3

24. Let’s add an “8”, and the new balance point will
be 5 . . . so that everything stays equal.
3 5
5
4 8

25. Let’s Return to the Technical Definition
3 5
5
4 8

26. Let’s Return to the Technical Definition
“The mean represents the balance point of the
distribution and takes into account the
weighted value of each observation”.
3 5
5
4 8

27. Let’s Return to the Technical Definition
“The mean represents the balance point of the
distribution and takes into account the
weighted value of each observation”.
3 5
5
4 8

28. Let’s focus on the next part of the definition
3 5
5
4 8

29. Let’s focus on the next part of the definition
“The mean represents the balance point of the
distribution and takes into account the
weighted value of each observation”.
3 5
5
4 8

30. Let’s focus on the next part of the definition
“The mean represents the balance point of the
distribution and takes into account the
weighted value of each observation”.
3 5
5
4 8

31. Because it is farther away from the balance
point, “8” is “weighted” more than the other
observations.
3 5
5
4 8

32. The number 8 is putting more pressure on the
teeter-totter because it is farther away from the
other numbers 3, 4, 5.
3 5
5
4 8

33. And you can tell that it is weighted more
because we had to move the balance from “4”
to “5” so the weight would remain equal on
both sides.
3 5
5
4 8

34. But, what if we change the number “8” to the
number “28”.
3 5
5
4 28

35. Then we would have to move our balance point
from “5” to “10” to keep everything balanced.

36. Then we would have to move our balance point
from “5” to “10” to keep everything balanced.
3 54 28
10

37. So here’s the definition again.
“The mean represents the balance point of the
distribution and takes into account the
weighted value of each observation”.
3 54 28
10

38. So here’s the definition again.
“The mean represents the balance point of the
distribution and takes into account the
weighted value of each observation”.
3 54 28
10

39. So here’s the definition again.
“The mean represents the balance point of the
distribution and takes into account the
weighted value of each observation”.
3 54 28
10

40. So here’s the definition again.
“The mean represents the balance point of the
distribution and takes into account the
weighted value of each observation”.
3 54 28
10

41. So here’s the definition again.
“The mean represents the balance point of the
distribution and takes into account the
weighted value of each observation”.
3 54 28
10

42. So what would happen to the mean if we added 100?

43. So what would happen to the mean if we added 100?
Your right. The mean or the balance point would move
much further to the right

44. As has probably become apparent – the mean of a
distribution is sensitive to the presence of outliers. For
example, compare

45. As has probably become apparent – the mean of a
distribution is sensitive to the presence of outliers. For
example, compare
5
5
4 83

46. As has probably become apparent – the mean of a
distribution is sensitive to the presence of outliers. For
example, compare
5
5
4 83
TO

47. As has probably become apparent – the mean of a
distribution is sensitive to the presence of outliers. For
example, compare
5
5
4 8
3 54
10
28
3
TO

48. As has probably become apparent – the mean of a
distribution is sensitive to the presence of outliers. For
example, compare
5
5
4 8
3 54
10
28
3
TO
The farther the
outlier is away
from rest of the
numbers the
more the mean
will be pulled
towards it.