
FREQUENCY DISTRIBUTION TABLES

FREQUENCY DISTRIBUTION GRAPHS

Frequency Distribution: Lists each
category (label) of data and the
number of occurrences.

Sum of all = population or sample size

Relative Frequency: The proportion of
occurrences for each category
Frequency
calculated as:
Sum _ of _ all _ frequencies
Sum of all = 1.

Bar Graph: Vertical or Horizontal. X-axis
contains the categories or labels. For
Frequency Distributions the y-axis is the
number of occurrances. For Relative
Frequency Distributions the y-axis is the
proportion (values between 0 and 1).
Bars do not need to be touching.
SPECIES
ZOO A
ZOO B
Elephant
6
3
Giraffe
12
7
Impala
13
24
Zebra
1
2
Ostrich
6
1
Guinea Hens
25
12
NUMBER
ZOO A ANIMAL INVENTORY
30
25
20
15
10
5
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SPECIES
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SPECIES
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NUMBER
NUMBER
30
25
20
15
10
5
0
El
G
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Im
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G
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O
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El
ZOO A ANIMAL INVENTORY
ZOO B ANIMAL INVENTORY
30
25
20
15
10
5
0
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SPECIES
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br
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O
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El
G
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NUMBER
ZOO A ANIMAL INVENTORY
30
25
20
15
10
5
0

CAN TREAT DISCRETE DATA LIKE
QUALITATIVE (IF ONLY SEVERAL VALUES)
OR AS WE WILL BE TREATING
CONTINUOUS DATA (IF MANY VALUES)

SEPARATE CONTINUOUS DATA INTO
CLASSES (INTERVALS) AND THEN DO
DISTRIBUTION TABLES OR GRAPHS
Frequency Distribution Table: Similar to
that for qualitative data, but each class
is for a value or an interval (range) of
values.
Histograms: Vertical bar graphs, where
the x-axis is the number line and each
bar is for a class. All bars must touch side
to side. Uses Lower Class limit on x-axis.

Cumulative Frequency Distributions: Each
class listed as before (lowest to largest), but
the frequencies are the total for that
frequency and all the lower classes.

Relative Cumulative Frequency Distribution:
Each Cumulative Frequency divided by
total of all frequencies. The last class will
have a cumulative value of 1.0
Use number of siblings
 Do as Frequency Table
 Do as Relative Frequency
 Do as Cumulative Frequency
 Do as Relative Cumulative Frequency


Class: An interval of numbers along the
number line.

Lower Class Limit (LCL): The beginning
number of the class.

Upper Class Limit (UCL): The last number
of the class.

Class Width: the difference between lower
class limits (or upper class limits), found by
taking using data set’s maximum and minimum
Maximum  Minimum
and calculating
#_ of _ Classes
rounding up to a convenient value

Midpoint of Each Class: The point in the middle
of the class, found by averaging the class
lower class limit and the next class lower class
limit.
1. Organize data in ascending order:
1.03
1.72
1.99
3.21
4.24
4.58
1.36
1.75
2.52
3.47
4.27
4.72
1.45
1.85
2.67
3.50
4.43
4.75
1.51
1.92
3.06
3.72
4.54
4.79
1.63
1.95
3.20
3.78
4.57
4.91
2. Determine the number of classes (5 –
20): For this we will use 6.
3. Find the maximum and minimum: For
this max = 4.91 and min = 1.03
4. Calculate the Class Width:
MAX  MIN  4.911.03  0.647
6
#_ of _ CLASSES
Round UP to a convenient value. We will
use 0.70.
5. Determine First Lower Class Limit: For this
we will use 1.00 (something convenient and
lower than the Minimum).
6. Determine the next 5 Lower Class Limits by
adding class width to the first and each
subsequent to get the next:
1.00+.70=1.70; 1.70+.70=2.40 …
3.10, 3.80, 4.50.
7. Determine the first Upper Class Limit by
Subtracting 1 from the last place of the
second Lower Class Limit: 1.70-.01=1.69.
8. Find the other 5 Upper Class Limits by
adding the class width to each previous
Upper Class Limits: 1.69+.7=2.39,
2.39+.7=3.09, …, 3.79, 4.49, 5.19
9. Now construct the Table ……:
CLASS
LOWER CLASS LIMIT
UPPER CLASS LIMIT
FREQUENCY
1.00
1.69
?
1.70
2.39
?
2.40
3.09
?
3.10
3.79
?
3.80
4.49
?
4.50
5.19
?
And count the frequencies in each class …:
1.03
1.72
1.99
3.21
4.24
4.58
1.36
1.75
2.52
3.47
4.27
4.72
1.45
1.85
2.67
3.50
4.43
4.75
1.51
1.92
3.06
3.72
4.54
4.79
1.63
1.95
3.20
3.78
4.57
4.91
And complete the Table:
CLASS
LOWER CLASS LIMIT
UPPER CLASS LIMIT
FREQUENCY
1.00
1.69
5
1.70
2.39
6
2.40
3.09
3
3.10
3.79
6
3.80
4.49
3
4.50
5.19
5
10. Draw the histogram:
Histogram
8
7
Frequency
6
5
4
3
2
1
0
1.00
1.70
2.40
3.10
LCL
3.80
4.50
5.3
5.8
6.4
7.1
5.5
5.9
6.6
7.1
5.6
6.2
6.6
7.3
5.7
6.3
6.7
7.6
5.7
6.3
6.8
7.9

Stem Leaf Plot: Used for recording and
showing dispersion of data. Stem can be
the integer portion of a number and the
leaves the decimal portion. Or the stem
could be the tens digit and the leaves the
ones digit.
5-3,5,6,7,7,8,9
 6-2,3,3,4,6,6,7,8
 7-1,1,3,6,9


Dot Plot: Also used to show dispersion of
data. Draw a number line and label the
horizontal scale with the numbers from
the data from lowest to highest. Then
place a dot above the numbers each
time the number occurs.
*
*
*
* * * * *
* *
|___|___|___|___|___|___|___|___|___|___|
5.3 5.4 5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3

Polygon Plot: Line graph using the
midpoints for the x-axis and frequencies
for the y-axis. Both ends of the line must
come back to the 0 on the y-axis.
POLYGON GRAPH
FREQUENCY
10
8
6
4
2
0
0
2
4
6
8
10 12 14 16 18 20 22 24
CLASS MIDPOINT

Given a Polygon Plot, construct a
Frequency Distribution Table.
› 1. Find the Class Width: Difference in Midpoints
› 2. Find first two LCL’s: Midpoint +/- ½*Class
Width
› 3. Find First Upper Class Limit: 2nd LCL – 1
› Find remainder of LCL’s & UCL’s
› Find each class’s frequency

Ogive (pronounced oh jive) Plot: Line
Graph used for displaying Cumulative
Frequency Distributions. The x-axis is the
Upper Class Limit and the y-axis is the
Cumulative Frequency. The first point is a
class width less than the first Upper Class
Limit so that the line starts with a
frequency of 0.

Ogive Plot:
22
20
18
16
14
12
10
8
6
4
2
0
1.99
2.99
3.99
4.99
5.99
6.99
7.99
8.99
9.99
10.99
11.99
12.99
13.99

Time Series Plots: Can be vertical or
horizontal bar graphs, or line graphs. Xaxis is time intervals or ages (years,
months, days) and y-axis is frequency.
NORMAL DISTRIBUTION
UNIFORM DISTRIBUTION
7
6
8
FREQUENCY
FREQUENCY
10
6
4
2
5
4
3
2
1
0
0
A
B
C
GRADE
D
F
A
B
C
GRADE
D
F
SKEWED LEFT DISTRIBUTE
12
12
10
10
FREQUENCY
FREQUENCY
SKEWED RIGHT DISTRIBUTE
8
6
4
8
6
4
2
2
0
0
A
B
C
GRADE
D
F
A
B
C
GRADE
D
F
Vertical Scale Manipulation: Not starting
the y-axis at 0. Also using a break in the
scale. Can make differences look
bigger than they really are.
 Exaggeration of Bars or Symbols: Used in
pictographs.
 Horizontal Scale Manipulation: Not all
classes or time interval are the same
width.


“Get your facts first, then you can distort
then as you please” Mark Twain

“There are lies, damn lies, and
STATISTICS” Mark Twain

“Definition of Statistics: The science of
producing unreliable facts from reliable
figures.” Evan Esar