{ "cells": [ { "cell_type": "markdown", "id": "79cd8c04", "metadata": {}, "source": [ "# Descriptive statistics\n", "\n", "pandas objects are equipped with a number of common mathematical and statistical methods. Most of them fall into the category of reductions or summary statistics, methods that extract a single value (such as the sum or mean) from a series or set of values from the rows or columns of a DataFrame. Compared to similar methods found in NumPy arrays, they also handle missing data." ] }, { "cell_type": "code", "execution_count": 1, "id": "1f4bf43c", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " 0 1 2\n", "2022-02-03 0.686507 1.870769 -0.699365\n", "2022-02-04 -1.462243 0.833043 0.423066\n", "2022-02-05 0.227436 -1.146793 -0.495678\n", "2022-02-06 0.404523 0.517117 -1.475375\n", "2022-02-07 2.022298 -0.263188 -0.478148\n", "2022-02-08 -0.056213 0.913033 -0.723379\n", "2022-02-09 NaN NaN NaN" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np\n", "import pandas as pd\n", "\n", "\n", "rng = np.random.default_rng()\n", "df = pd.DataFrame(\n", " rng.normal(size=(7, 3)), index=pd.date_range(\"2022-02-02\", periods=7)\n", ")\n", "new_index = pd.date_range(\"2022-02-03\", periods=7)\n", "df2 = df.reindex(new_index)\n", "\n", "df2" ] }, { "cell_type": "markdown", "id": "b1cb2575", "metadata": {}, "source": [ "Calling the `pandas.DataFrame.sum` method returns a series containing column totals:" ] }, { "cell_type": "code", "execution_count": 2, "id": "070b5cd2", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0 1.822307\n", "1 2.723981\n", "2 -3.448879\n", "dtype: float64" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df2.sum()" ] }, { "cell_type": "markdown", "id": "b7884bef", "metadata": {}, "source": [ "Passing `axis='columns'` or `axis=1` instead sums over the columns:" ] }, { "cell_type": "code", "execution_count": 3, "id": "1293360b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2022-02-03 1.857911\n", "2022-02-04 -0.206135\n", "2022-02-05 -1.415035\n", "2022-02-06 -0.553735\n", "2022-02-07 1.280962\n", "2022-02-08 0.133441\n", "2022-02-09 0.000000\n", "Freq: D, dtype: float64" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df2.sum(axis=\"columns\")" ] }, { "cell_type": "markdown", "id": "ec346926", "metadata": {}, "source": [ "If an entire row or column contains all NA values, the sum is `0`. This can be disabled with the `skipna` option:" ] }, { "cell_type": "code", "execution_count": 4, "id": "f698747c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2022-02-03 1.857911\n", "2022-02-04 -0.206135\n", "2022-02-05 -1.415035\n", "2022-02-06 -0.553735\n", "2022-02-07 1.280962\n", "2022-02-08 0.133441\n", "2022-02-09 NaN\n", "Freq: D, dtype: float64" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df2.sum(axis=\"columns\", skipna=False)" ] }, { "cell_type": "markdown", "id": "644a61ca", "metadata": {}, "source": [ "Some aggregations, such as `mean`, require at least one non-`NaN` value to obtain a valuable result:" ] }, { "cell_type": "code", "execution_count": 5, "id": "1c799ec9", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2022-02-03 0.619304\n", "2022-02-04 -0.068712\n", "2022-02-05 -0.471678\n", "2022-02-06 -0.184578\n", "2022-02-07 0.426987\n", "2022-02-08 0.044480\n", "2022-02-09 NaN\n", "Freq: D, dtype: float64" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df2.mean(axis=\"columns\")" ] }, { "cell_type": "markdown", "id": "ce078db0", "metadata": {}, "source": [ "## Options for reduction methods\n", "\n", "Method | Description\n", ":----- | :----------\n", "`axis` | the axis of values to reduce: `0` for the rows of the DataFrame and `1` for the columns\n", "`skipna` | exclude missing values; by default `True`.\n", "`level` | reduce grouped by level if the axis is hierarchically indexed (MultiIndex)\n", "\n", "Some methods, such as `idxmin` and `idxmax`, provide indirect statistics such as the index value at which the minimum or maximum value is reached:" ] }, { "cell_type": "code", "execution_count": 6, "id": "aa6e4b54", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0 2022-02-07\n", "1 2022-02-03\n", "2 2022-02-04\n", "dtype: datetime64[ns]" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df2.idxmax()" ] }, { "cell_type": "markdown", "id": "ad8181d8", "metadata": {}, "source": [ "Other methods are accumulations:" ] }, { "cell_type": "code", "execution_count": 7, "id": "373b127a", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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012
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" ], "text/plain": [ " 0 1 2\n", "2022-02-03 0.686507 1.870769 -0.699365\n", "2022-02-04 -0.775736 2.703812 -0.276300\n", "2022-02-05 -0.548300 1.557019 -0.771977\n", "2022-02-06 -0.143777 2.074136 -2.247352\n", "2022-02-07 1.878520 1.810948 -2.725500\n", "2022-02-08 1.822307 2.723981 -3.448879\n", "2022-02-09 NaN NaN NaN" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df2.cumsum()" ] }, { "cell_type": "markdown", "id": "4603de28", "metadata": {}, "source": [ "Another type of method is neither reductions nor accumulations. `describe` is one such example that produces several summary statistics in one go:" ] }, { "cell_type": "code", "execution_count": 8, "id": "010fb833", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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012
count6.0000006.0000006.000000
mean0.3037180.453997-0.574813
std1.1282011.0433120.609912
min-1.462243-1.146793-1.475375
25%0.014699-0.068112-0.717375
50%0.3159790.675080-0.597521
75%0.6160110.893035-0.482530
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" ], "text/plain": [ " 0 1 2\n", "count 6.000000 6.000000 6.000000\n", "mean 0.303718 0.453997 -0.574813\n", "std 1.128201 1.043312 0.609912\n", "min -1.462243 -1.146793 -1.475375\n", "25% 0.014699 -0.068112 -0.717375\n", "50% 0.315979 0.675080 -0.597521\n", "75% 0.616011 0.893035 -0.482530\n", "max 2.022298 1.870769 0.423066" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df2.describe()" ] }, { "cell_type": "markdown", "id": "5d1f2a90", "metadata": {}, "source": [ "For non-numeric data, `describe` generates alternative summary statistics:" ] }, { "cell_type": "code", "execution_count": 9, "id": "4277fda3", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
CodeOctal
count66
unique65
topU+0000004
freq12
\n", "
" ], "text/plain": [ " Code Octal\n", "count 6 6\n", "unique 6 5\n", "top U+0000 004\n", "freq 1 2" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "data = {\n", " \"Code\": [\"U+0000\", \"U+0001\", \"U+0002\", \"U+0003\", \"U+0004\", \"U+0005\"],\n", " \"Octal\": [\"001\", \"002\", \"003\", \"004\", \"004\", \"005\"],\n", "}\n", "df3 = pd.DataFrame(data)\n", "\n", "df3.describe()" ] }, { "cell_type": "markdown", "id": "ce69eb28", "metadata": {}, "source": [ "Descriptive and summary statistics:\n", "\n", "Method | Description\n", ":----- | :----------\n", "`count` | number of non-NA values\n", "`describe` | calculation of a set of summary statistics for series or each DataFrame column\n", "`min`, `max` | calculation of minimum and maximum values\n", "`argmin`, `argmax` | calculation of the index points (integers) at which the minimum or maximum value was reached\n", "`idxmin`, `idxmax` | calculation of the index labels at which the minimum or maximum values were reached\n", "`quantile` | calculation of the sample quantile in the range from 0 to 1\n", "`sum` | sum of the values\n", "`mean` | arithmetic mean of the values\n", "`median` | arithmetic median (50% quantile) of the values\n", "`mad` | mean absolute deviation from the mean value\n", "`prod` | product of all values\n", "`var` | sample variance of the values\n", "`std` | sample standard deviation of the values\n", "`skew` | sample skewness (third moment) of the values\n", "`kurt` | sample kurtosis (fourth moment) of the values\n", "`cumsum` | cumulative sum of the values\n", "`cummin`, `cummax` | cumulated minimum and maximum of the values respectively\n", "`cumprod` | cumulated product of the values\n", "`diff` | calculation of the first arithmetic difference (useful for time series)\n", "`pct_change` | calculation of the percentage changes" ] }, { "cell_type": "markdown", "id": "317bdb46", "metadata": {}, "source": [ "## `ydata-profiling`\n", "\n", "[ydata-profiling](https://docs.profiling.ydata.ai/latest/) generates profile reports from a pandas DataFrame. The pandas `df.describe()` function is handy, but a bit basic for exploratory data analysis. ydata-profiling extends pandas DataFrame with `df.profile_report()`, which automatically generates a standardised report for understanding the data." ] }, { "cell_type": "markdown", "id": "5cde7e28", "metadata": {}, "source": [ "### Installation\n", "\n", "```bash\n", "$ uv add \"ydata-profiling[notebook, unicode]\"\n", "…\n", "Resolved 170 packages in 59ms\n", "Installed 68 packages in 265ms\n", " + annotated-types==0.7.0\n", " + anyio==4.6.2.post1\n", " + appnope==0.1.4\n", "…\n", " + websocket-client==1.8.0\n", " + wordcloud==1.9.3\n", " + ydata-profiling==4.12.0\n", "$ uv run --with jupyter jupyter nbextension enable --py widgetsnbextension\n", "Enabling notebook extension jupyter-js-widgets/extension...\n", " - Validating: OK\n", "```" ] }, { "cell_type": "markdown", "id": "9da36ef5", "metadata": {}, "source": [ "### Example" ] }, { "cell_type": "code", "execution_count": 10, "id": "2bb967a2", "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "1393518e8a284bb88249c69742336dcd", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Summarize dataset: 0%| | 0/5 [00:00Unique" } }, "0010dc59eb1545b589c0bb64d9bc1e45": { "model_module": "@jupyter-widgets/base", "model_module_version": "1.2.0", "model_name": "LayoutModel", "state": { "grid_area": "widget007" } }, "0011d436b61d4d97ab7b5a80db0b2ec4": { "model_module": "@jupyter-widgets/controls", "model_module_version": "1.5.0", "model_name": "FloatProgressModel", "state": { "layout": "IPY_MODEL_0a41d329b44b495788d3514cfef86d75", "max": 891, "style": "IPY_MODEL_1949c383616d4048938d82c99842dd34", "value": 5 } }, "0012a088f34648848506f3d95205e33c": { "model_module": "@jupyter-widgets/base", "model_module_version": "1.2.0", "model_name": "LayoutModel", "state": {} }, "0012a62d97394992846f35d45e905c61": { "model_module": "@jupyter-widgets/base", "model_module_version": 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\n SibSp\n
\n Real number (ℝ)\n

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Histogram of lengths of the category

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\n Real number (ℝ)\n

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\n Ticket\n
\n Categorical\n

\n

\n HIGH CARDINALITY \n UNIFORM \n

\n

\n \n

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\n 1\n
\n Real number (ℝ)\n

\n

\n MISSING \n

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\n Sex\n
\n Categorical\n

\n

\n HIGH CORRELATION \n

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\n Cabin\n
\n Categorical\n

\n

\n HIGH CARDINALITY \n MISSING \n

\n

\n \n

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\n

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\n

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\n Ticket\n
\n Categorical\n

\n

\n HIGH CORRELATION \n UNIFORM \n UNIQUE \n

\n

\n \n

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\n 2\n
\n Real number (ℝ)\n

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\n Age\n
\n Real number (ℝ)\n

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\n Parch\n
\n Real number (ℝ)\n

\n

\n \n

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\n Survived\n
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\n Real number (ℝ)\n

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\n Name\n
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\n

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Nullity matrix is a data-dense display which lets you quickly visually pick out patterns in data completion.

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\n Survived\n
\n Real number (ℝ)\n

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