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Frequency Distributions
Frequency Distributions
Frequency Distribution Table:
Shows classes (intervals, buckets) of data with the frequency (count) of the number of entries in each class.
Frequency Distributions
Class Frequency
1 - 5 3
6 - 10 5
11 - 15 4
16 - 20 2
21 - 25 1
Class Limits:Each class has an upper and lower limit. In this example: 1 is the lower class limit of the first class, and 5 is the upper class limit of the first class.
Frequency Distributions
Class Frequency
1 - 5 3
6 - 10 5
11 - 15 4
16 - 20 2
21 - 25 1
Class Width:The class width is the difference between the upper limits (or the lower limits) of adjacent classes.
In this example, the class width is 6 – 1 = 5
Frequency Distributions
Class Frequency
1 - 5 3
6 - 10 5
11 - 15 4
16 - 20 2
21 - 25 1
Class width6 - 1= 5
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Frequency Distributions
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Frequency Distributions
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Frequency Distributions
class tally f
67 – 78
79 - 90
91 - 102
103 - 114
115 - 126
Frequency distribution with 5 classes
Min: 67; Max: 125; Classes: 5
Class Width: (125 – 67)/5 = 11.6 → 12
Lower Class Limits:67, 79, 91, 103, 115
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Frequency Distributions
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Frequency Distributions
Class Midpoint: (lower limit + upper limit)/2
Notice the difference between the midpoints of consecutive classes is the class width.
84.5 – 72.5 = 1296.5 – 84.5 = 12
class midpoint f
67 – 78 (67 + 78)/2 = 72.5
3
79 - 90 (79+90)/2= 84.5
5
91 - 102 (91 + 102)/2= 96.5
8
103 - 114 (103 + 114)/2= 108.5
9
115 - 126 (115 + 126)/2= 120.5
5
30
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Frequency Distributions
Relative Frequency of a Class Portion of the whole in the class
Relative Frequency = f/n
class f Relative freq
67 – 78 3 3/30 = 1/10
79 - 90 5 5/30 =1/6
91 - 102 8 8/30 =4/15
103 - 114 9 9/30 =3/10
115 - 126 5 5/30
n = 30
30/30 = 1
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Frequency Distributions
Cumulative Frequency
The sum of the frequency of current class and all lower classes.
Think of it as a running total.
class f Cumulative Freq
67 – 78 3 3
79 - 90 5 8
91 - 102 8 16
103 - 114 9 25
115 - 126 5 30
n = 30
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Frequency Distributions
Expanded Frequency Distribution class f midpoint Relative freq Cumulative
freq
67 – 78 3 72.5 .10 3
79 - 90 5 84.5 .17 8
91 - 102 8 96.5 .27 16
103 - 114 9 108.5 .30 25
115 - 126 5 120.5 .17 30
n = 30
1.01 (rounding)
Midpoint = (lower limit + upper limit)/2
Relative Frequency = f/n
Cumulative Frequency:Number of values in that class or lower
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Frequency Distributions
Class Boundaries separate the data values in a class without being a data value in the class. Boundaries are usually set at one-half the precision of your data. For whole number values, we back off 0.5 in each direction:
class f Class Boundaries
67 – 78
3 66.5 – 78.5
79 - 90
5 78.5 – 90.5
91 - 102
8 90.5 – 102.5
103 - 114
8 102.5 – 114.5
115 - 126
5 114.5 – 126.5
n = 30
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Frequency Distributions
Class Boundaries
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Frequency Distributions
Class Boundaries
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Frequency Distributions
Frequency Histogram ● Bar graph of data classes on the horizontal axis vs frequency or relative frequency on the vertical
● The bars must touch
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Frequency Distributions
class limits
class midpoints
class boundaries
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Frequency Distributions
Frequency Histogramby class boundaries
This is the from most college texts will use.
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Frequency Distributions
By Class Limits
Online generators often use this form.
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Frequency Distributions
By Midpoints
Allows one to think of each bar as a count of a representative value for calculation purposes.
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Frequency Distributions
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Frequency Distributions
3
5
89
5
Typically the final product does not contain the bars.
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Frequency Distributions
Relative Frequency Histogram has the relative frequency as the
vertical axis.
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Frequency Distributions
Ogive Shows cumulative frequency at the upper class boundaries
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Frequency Distributions
Key: 6 | 7 = 67
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Frequency Distributions
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Frequency Distributions
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Data
Distributions of Data Sets: Shape
Some shapes of distributions are symmetric, uniform, skew right and skew left.
These are ideal models. With real data, you probably won’t get distributions that fit perfectly, but we will use these models as a general description.
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Data
Distributions of Data Sets: Shape
Shape of distributions: symmetric:
Also called bell shaped or nearly normal. The mean median,and mode are equal in a symmetric distribution.
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Data
Distributions of Data Sets: Shape
Shape of distribution: uniform
All entries or classes have equal frequencies. The mean And median are the same
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Data
Distributions of Data Sets: Shape
Shape of distribution: skew left
The “tail” is on the left. The mean is left of the median andThe mode.
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Data
Distributions of Data Sets: Shape
Shape of distribution: skew right
The “tail” is on the right. The mean is right of the median and the mode.
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Frequency Distributions
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