Measures of Central Tendency


Mean: average- the evening or leveling out of data. “take from the
rich, give to the poor.”
You add up all the data and divide by the number of pieces of data you
have.

Mode: number that occurs the most. There can be one mode, no mode,
or many modes.
o 32, 40, 56, 70, 48, 32 – mode is 32
o 45, 67, 90, 45, 23, 67, 36- mode is 45 and 67
o 67, 32, 48, 35, 53, 56 – no mode

Median: middle number in a set of data after data has been arranged
from least to greatest. In an even set, the mean of the two middle
numbers.
o 107, 99, 52, 85, 76. *rearrange data from least to greatest*
52, 76, 85, 99, 107 - 85 is median
o 107, 99, 52, 89, 76, 85. *rearrange from least to greatest*
52, 76, 85, 89, 99, 107 – add two middle numbers together and
divide by 2 *85 +89 = 174 /2= 87

Range: the difference between the smallest and largest values in a set
of data (think of a mountain range).
o 107, 99, 52, 89. 76, 85
Rearrange them in order from least to greatest.
52, 76, 85, 89, 99, 107
Take the greatest value and subtract the lowest
o 107-52 = 55

Outlier- a value in a set of data that is much larger or much smaller
than the other values in the set of data.
o 107, 99, 52, 89, 85, 2
o 2 is the outlier because is it much smaller than the second
smallest piece of data.
Creating a Set of Data for a Given Mean
Provide 5 pieces of data for a mean of 25
25
25
25
25
25
-5
-8
+5
+6
+2
20
17
30
31
27
New data set whose mean is 25: 20, 17, 30, 31, 27
Method 1:
 Multiply the given mean by the # of pieces of data
o 25 x 5 = 125
 After you have EQUALLY added and subtracted from the
given numbers, add up the values from the new data set and
make sure that they have the same answer as the 25 x 5=
125
o 20 + 17 + 30 + 31 + 27 = 125
Method 2:
 Multiply the given mean by the number of pieces of data.
o 25 x 5 = 125
 You can split the number you get into any combination of 5
numbers that add up to it (125).
 Example 1: 70
15
10
5
20
 Example 2: 40
35
25
15 10
Constructing a Line Plot (DADD)
A line plot is a display of data on a horizontal line (x-axis). The
data is displayed vertically with Xs.
 You can visualize clusters/groups
 Mode is easily seen
EXAMPLE: The children in Ms. Storz’s class were polled to find
the number of siblings they had.
Data: 4, 2, 1, 1, 2, 3, 4, 5, 4, 4, 2, 2, 5, 3, 3, 2, 7
3). Arrange data in order from least to greatest:
1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 7
4). When you put the Xs on the line plot- they have to be the
same size and spaced the same.
Ms. Storz’s Class
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
1
2
3
4
5
Number of Siblings
X
6
7
Constructing a Line Plot (DADD)
Draw a horizontal line with arrows to display the data (x-axis) – line plots
above and below do not have arrows  but you must include them.
Assign a title (both the graph and the x-axis)
Determine the RANGE of data (minimum and maximum)
 Place ALL numbers on the line (even if not in the data).
 Equally space out the numbers and arrows.
Draw an X above the corresponding data (x – same size)
Measures of Central Tendency from a Line Plot
Ms. Storz’s Class Siblings
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
1
2
3
4
5
X
6
7
Number of Siblings
 Mode: Tallest Tower - 2
 Median: cross off high, low until you get to the middle - 3
 Range: subtract the lowest value from the highest
o 7-1=6
Range= 6
 Mean:
1. Multiply the number of Xs by the given data value
(Data Value) x (number of Xs)
1 x2= 2
2 x 5= 10
4x4= 16
5x2= 10
3 x 3= 9
7x1=7
2. The add all the values together.
1+ 10+ 9+ 12+ 10 + 7 = 49
3. Then divide the sum by the number of Xs.
49 ÷ 17 = 2.88
Constructing a Stem and Leaf Plot (SMACK)
Sequence Data (in order from least to greatest)
Make an outline
Assign a title
Chart stem and leaf values (in order/ line up vertically)
Key
Example:
Ms. Storz’s students scored the following on their recent math
test: 97, 65, 87, 75, 84, 95, 92, 74, 83, 87, 91, 76, 80, 68, 87,
90, 76, 90, 92, 87
Construct a Stem and Leaf Plot to display the scores.
1. Sequence Data: 65, 68, 74, 75, 76, 76, 80, 83, 84,
87,87,87,87, 90,90,91,92, 92, 95,97.
2. Make an outline.
3. Assign a title
4. Chart stem and leaf values: determine stems by finding the
least and greatest tens. All possible stems must be included
5. Key
Ms. Storz’s Class Math Test Scores
Stems (10s) Leaves (1s)
6
7
8
9
5
4
0
0
8
5 6 6
3 4 7 7 7 7
0 1 2 2 5 7
Key 6 5 means 65
Calculating the Measures of Central Tendency (MCTs) from a
Stem and Leaf Plot
RANGE = (Largest Value) – (Smallest Value)
 Largest Value: find the largest STEM and go out to the largest LEAF
in that column
 Smallest Value: Find the smallest STEM and the LEAF that is closest
to the stem (smallest digit number)
79 – 30 = 49
Range = 49
MODE = find the LEAF that appears most often in A ROW. REMEMBER,
that digit is NOT the actual value. Make sure you match up your leaf (1s)
with it’s stem (10s) to get the true value.
Mode = 56
MEDIAN = HIGH, LOW. You go from the highest LEAF to the lowest
LEAF. DO NOT include the stems when you are crossing off numbers!
MEDIAN = 56
MEAN = You have to ADD UP all the VALUES (remember to match up the
leaf with its stem to get its TRUE VALUE) and DIVIDE by the number of
LEAVES.
 Find the value of each row of data
 Add all the rows together
64
 Divide by the number of leaves
130
226 839 ÷ 15 = 55.93
261
Quiz Scores
+ 158
839
Stems (10s)
3
4
5
6
7
Leaves (1s)
0
1
6
2
9
4
64
2 7
130
6 6 8
226
5 5 9
261
9
158
Key 4 1 means 41
Mean = 55.93






Back to Back Stem and Leaf Plot
Compares two sets of similar data. One side “versus” the other.
Both the right and left sides share the stems.
Right side is just like a regular stem and leaf plot; the left side is a “mirror image”
of the right.
TWO KEYS
Leaves are labeled by the two things being compared.
Still use S.M.A.C.K. to construct the line plot.
Ms. Storz’s Class
Number of Snaps in 30 Seconds
Left Side
Right Side
60
69
97
81
59
59
58
72
64
67
62
32
66
58
69
61
61
62
53
80
75
64
62
63
77
75
53
62
65
65
65
67
49
67
50
64
58
66
41
56
46
79
69
85
Sequence Data:
Sequence Data:
32, 53, 58, 58, 59, 59, 60, 61, 61, 62, 62,
41, 46, 49, 50, 53, 56, 58, 62, 62, 63, 64,
64, 64, 66, 67, 69, 69, 72, 75, 80, 81, 97
65, 65, 65, 66, 67, 67, 69, 75, 77, 79, 85
Ms. Storz’s Class
Number of Snaps in 30 Seconds
Left Hand
Stems
2
9 9 8 8 3
9 9 7 6 4 4 2 2 1 1 0
5 2
1 0
7
Key 2 3 means 32
3
4
5
6
7
8
9
Right Hand
1
0
2
5
5
6 9
3 6 8
2 3 4 5 5 5 67 7 9
7 9
85
Key 4 1 means 41
Ms. Storz’s Class
Number of Snaps in 30 Seconds
Left Hand
Stems
2
9 9 8 8 3
9 9 7 6 4 4 2 2 1 1 0
5 2
1 0
7
Key 2 3 means 32
Left Side:
Mean: _____
Median: 64
Mode: 58, 59, 61, 62, 64, 69
Range:97-32= 65
3
4
5
6
7
8
9
Right Hand
1 6 9
136
0 3 6 8
214
2 2 3 4 5 5 5 6 7 7 9715
5 7 9 231
5 85
MEAN
136
214
Key 4 1 means 41
715
231
+ 85
1,381
Right Side:
Mean: 62.78
1,381 ÷ 22=
Median: 64.5
62.78
Mode: 65
Range: 85-41= 44