Frequency Tables

Section 2.1 Frequency Tables

One way to describe a variable is a frequency table, which contains the values of the variable and their frequencies — that is, the number of times each value appears. This description is called the distribution of the variable.

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To represent distributions, we’ll use a library called empiricaldist. In this context, "empirical" means that the distributions are based on data rather than mathematical models. empiricaldist provides a class called FreqTab that we can use to compute and plot frequency tables. We can import it like this.

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Listing 2.1.1. Python Code

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from empiricaldist import FreqTab

To show how it works, we’ll start with a small list of values.

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Listing 2.1.2. Python Code

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t = [1.0, 2.0, 2.0, 3.0, 5.0]

FreqTab provides a method called from_seq that takes a sequence and makes a FreqTab object.

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Listing 2.1.3. Python Code

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$ ftab = FreqTab.from_seq(t)
ftab
1.0    1
2.0    2
3.0    1
5.0    1
Name: , dtype: int64

A FreqTab object is a kind of Pandas Series that contains values and their frequencies. In this example, the value 1.0 has frequency 1, the value 2.0 has frequency 2, etc.

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FreqTab provides a method called bar that plots the frequency table as a bar chart.

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Listing 2.1.4. Python Code

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ftab.bar()
decorate(xlabel="Value", ylabel="Frequency")

Because a FreqTab is a Pandas Series, we can use the bracket operator to look up a value and get its frequency.

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Listing 2.1.6. Python Code

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$ ftab[2.0]
np.int64(2)

But unlike a Pandas Series, we can also call a FreqTab object like a function to look up a value.

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Listing 2.1.7. Python Code

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$ ftab(2.0)
np.int64(2)

If we look up a value that does not appear in the FreqTab, the function syntax returns 0.

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Listing 2.1.8. Python Code

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$ ftab(4.0)
0

A FreqTab object has an attribute called qs that returns an array of values — qs stands for quantities, although technically not all values are quantities.

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Listing 2.1.9. Python Code

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$ ftab.qs
array([1., 2., 3., 5.])

FreqTab also has an attribute called fs that returns an array of frequencies.

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Listing 2.1.10. Python Code

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$ ftab.fs
array([1, 2, 1, 1])

FreqTab provides an items method we can use to loop through quantity-frequency pairs:

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Listing 2.1.11. Python Code

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$ for x, freq in ftab.items():
    print(x, freq)
1.0 1
2.0 2
3.0 1
5.0 1

We’ll see more FreqTab methods as we go along.

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