Statistics¶

This section showcases the utility functions found in the datachart.utils.stats module.

Let us start by importing the supporting libraries:

In [1]:

import random

import random

Statistics Submodule¶

The dataset.utils.stats submodule contains functions for calculating statistics. To showcase its use, let us create a list of random numbers:

In [2]:

random_values = random.sample(range(1, 100), 10)
random_values

random_values = random.sample(range(1, 100), 10) random_values

Out[2]:

[13, 85, 35, 65, 18, 90, 7, 39, 8, 64]

Let us now showcase the functions in the stats module.

Count¶

The count function returns the number of elements in the list.

In [3]:

from datachart.utils.stats import count

from datachart.utils.stats import count

In [4]:

count(random_values)

count(random_values)

Out[4]:

10

Sum¶

The sum_values function returns the sum of all values in the list.

In [5]:

from datachart.utils.stats import sum_values

from datachart.utils.stats import sum_values

In [6]:

sum_values(random_values)

sum_values(random_values)

Out[6]:

424.0

Mean¶

The mean function returns the mean of the values.

In [7]:

from datachart.utils.stats import mean

from datachart.utils.stats import mean

In [8]:

mean(random_values)

mean(random_values)

Out[8]:

42.4

Median¶

The median function returns the median of the values.

In [9]:

from datachart.utils.stats import median

from datachart.utils.stats import median

In [10]:

median(random_values)

median(random_values)

Out[10]:

37.0

Standard Deviation¶

The stdev function returns the standard deviation of the values.

In [11]:

from datachart.utils.stats import stdev

from datachart.utils.stats import stdev

In [12]:

stdev(random_values)

stdev(random_values)

Out[12]:

30.033980755138003

Variance¶

The variance function returns the variance of the values. Variance is the square of the standard deviation.

In [13]:

from datachart.utils.stats import variance

from datachart.utils.stats import variance

In [14]:

variance(random_values)

variance(random_values)

Out[14]:

902.04

Quantile¶

The quantile function returns the quantile of the values.

In [15]:

from datachart.utils.stats import quantile

from datachart.utils.stats import quantile

Show the 25th quantile:

In [16]:

quantile(random_values, 25)

quantile(random_values, 25)

Out[16]:

14.25

Show the 75th quantile:

In [17]:

quantile(random_values, 75)

quantile(random_values, 75)

Out[17]:

64.75

Interquartile Range (IQR)¶

The iqr function returns the interquartile range, which is the difference between the 75th percentile (Q3) and 25th percentile (Q1). It is useful for identifying outliers and understanding the spread of the middle 50% of the data.

In [18]:

from datachart.utils.stats import iqr

from datachart.utils.stats import iqr

In [19]:

iqr(random_values)

iqr(random_values)

Out[19]:

50.5

Minimum¶

The minimum function returns the minimum of the values.

In [20]:

from datachart.utils.stats import minimum

from datachart.utils.stats import minimum

In [21]:

minimum(random_values)

minimum(random_values)

Out[21]:

7.0

Maximum¶

The maximum function returns the maximum of the values.

In [22]:

from datachart.utils.stats import maximum

from datachart.utils.stats import maximum

In [23]:

maximum(random_values)

maximum(random_values)

Out[23]:

90.0

Correlation¶

The correlation function calculates the Pearson correlation coefficient between two lists of values. It measures the linear relationship between the datasets, ranging from -1 (perfect negative correlation) to 1 (perfect positive correlation).

In [24]:

from datachart.utils.stats import correlation

from datachart.utils.stats import correlation

Create a second list of random values to compare:

In [25]:

random_values_2 = random.sample(range(1, 100), 10)
random_values_2

random_values_2 = random.sample(range(1, 100), 10) random_values_2

Out[25]:

[52, 53, 33, 14, 97, 34, 63, 46, 50, 2]

In [26]:

correlation(random_values, random_values_2)

correlation(random_values, random_values_2)

Out[26]:

-0.5346380232911461

Kernel density estimate¶

The kde1d function estimates the density of a list of values with a Gaussian kernel and returns it as {x, y} points, ready to draw as a datachart.charts.LineChart — over a density datachart.charts.Histogram of the same values, for instance. The bandwidth is a rule of datachart.constants.BANDWIDTH or a scalar factor, gridsize the number of points, and cut how many bandwidths the curve extends past the extremes (xlim fixes the range instead).

In [27]:

from datachart.utils.stats import kde1d

from datachart.utils.stats import kde1d

In [28]:

curve = kde1d(random_values, gridsize=5)
curve

curve = kde1d(random_values, gridsize=5) curve

Out[28]:

[{'x': -52.925669969227435, 'y': 5.369685049671554e-05},
 {'x': -2.212834984613714, 'y': 0.006844798655948651},
 {'x': 48.50000000000001, 'y': 0.008398528668814874},
 {'x': 99.21283498461372, 'y': 0.004262640825392958},
 {'x': 149.92566996922744, 'y': 3.276375337326581e-05}]

The kde2d function does the same for (x, y) points and returns the {x, y, z} surface a datachart.charts.ContourChart draws — the density contours of a scattered dataset. The gridsize can be one number or an (x, y) pair of column and row counts, and xlim/ylim fix the grid so several surfaces share it.

In [29]:

from datachart.utils.stats import kde2d

from datachart.utils.stats import kde2d

In [30]:

surface = kde2d(random_values, random_values_2, gridsize=3)
surface

surface = kde2d(random_values, random_values_2, gridsize=3) surface

Out[30]:

{'x': [-57.706250018619315, 48.499999999999986, 154.7062500186193],
 'y': [-51.81086115238257, 49.500000000000014, 150.81086115238259],
 'z': [[9.2260055480947e-23, 1.2759816599495725e-08, 7.1680617633241185e-09],
  [9.96560240175761e-08, 9.364386505251947e-05, 5.830277412765298e-08],
  [4.278774194643878e-08, 9.254928689045964e-10, 5.505654139376627e-23]]}

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