Measur es of Cent r al
Tendenc y
Mode: The most frequently occurring
score.
Median: middle score
When data is placed in order…
- half of the data will fall below
the median
- half of the data will fall above
the median
Data Set: 1, 8, 3, 9, 10, 12, 4
Step One: Reorder data
1, 3, 4, 8, 9, 10, 12
Step Two: Find the mid-point
1, 3, 4, 8, 9, 10, 12
To find the midpoint...
n+1
2
Will give you the place along
the string of ascending numbers
that holds the midpoint.
Our data set:
1, 3, 4, 8, 9, 10, 12
n=7
So...
n+1 = 7+1
2
2
th
The median will be in the 4 place along
the ascending string of numbers.
Our data set:
1, 3, 4, 8, 9, 10, 12
4th place
Median = 8
What about when n is an even number?
Data set:
1, 3, 4, 6, 7, 8, 8, 10
n=8
n + 1 = 4.5
2
1, 3, 4, 6, 7, 8, 8, 10
n=8
n + 1 = 4.5
2
This means that the median falls half
way between the 4th and 5th scores.
th
th
Average the 4 and 5 scores.
Dat a set :
1, 3, 4, 6, 7, 8, 8, 10
The 4
th
sc or e is
The 5 t h sc or e is
6
7
6 + 7 = 6.5
2
The median, in this case,
Is 6.5.
Data set:
1, 2, 4, 8, 10, 10, 30, 35
1, 2, 4, 8, 10, 10, 30, 35
n=8
n + 1 = 4.5
2
1, 2, 4, 8, 10, 10, 30, 35
th
The 4 score is 8
th
The 5 score is 10
The average of these two scores:
Median = 9
Mean: the average score of a data set.
Formula:
X
n
Data Set:
1, 3, 4, 8, 9, 10, 12
 X = 47
n=7
X
n
=
Mean = 6.71
47
7
X
: s y m b o l fo r th e m e a n
o f a s a m p le .
 : s y m b o l fo r th e m e a n
o f th e p o p u la tio n .
grades
f
cf
30
3
73
29.5
5
70
29
5
65
28.5
2
60
28
10
58
27.5
5
48
27
6
43
26.5
5
37
26
6
32
25
2
26
24.5
3
24
24
4
21
23.5
1
17
23
5
16
22.5
4
11
22
1
7
21.5
2
6
21
1
4
20
3
3
Mode:
28
grades
cf
f
30
3
73
29.5
5
70
29
5
65
28.5
2
60
28
10
58
27.5
5
48
27
6
43
26.5
5
37
26
6
32
25
2
26
24.5
3
24
24
4
21
23.5
1
17
23
5
16
22.5
4
11
22
1
7
21.5
2
6
21
1
4
20
3
3
Median: 26.5
n = 73
n+1
= 37
2
The 37th score is…
grades
cf
f
30
3
73
29.5
5
70
29
5
65
28.5
2
60
28
10
58
27.5
5
48
27
6
43
26.5
5
37
26
6
32
25
2
26
24.5
3
24
24
4
21
23.5
1
17
23
5
16
22.5
4
11
22
1
7
21.5
2
6
21
1
4
20
3
3
Mean:
X
X =
n
grades
 X  fX
 X  90  147.5  145  ...
f
fX
30
3
90
29.5
5
147.5
29
5
145
28.5
2
57
28
10
280
27.5
5
137.5
27
6
162
26.5
5
132.5
26
6
156
25
2
50
24.5
3
73.5
24
4
96
23.5
1
23.5
23
5
115
22.5
4
90
22
1
22
21.5
2
43
21
1
21
20
3
60
 X  1901.5
grades
cf
f
30
3
73
29.5
5
70
29
5
65
28.5
2
60
28
10
58
27.5
5
48
27
6
43
26.5
5
37
26
6
32
25
2
26
24.5
3
24
24
4
21
23.5
1
17
23
5
16
22.5
4
11
22
1
7
21.5
2
6
21
1
4
20
3
3
Mean:
26.05
X
X =
n
1901.5
=
73
Median, mean, mode
mode
mode
median
mean
median
mode
mean