{
  "source_file": "0930",
  "source_platform": "Medium",
  "author": "Kurtis Pykes",
  "title_listed": "The Basic Essentials: Statistics For Machine Learning",
  "keywords": "统计,ML基础",
  "domain": "机器学习",
  "content_type": "深度技术解析",
  "is_paid_flag": "部分免费/会员墙",
  "url": "https://towardsdatascience.com/the-basic-essentials-statistics-for-machine-learning-dd9cfeb0e5ef/",
  "publish_date": "2022-03",
  "corpus_stage": "预训练/SFT",
  "notes": "",
  "id": "ba0f50b1927f",
  "collected_at": "2026-10-02T00:11:37",
  "title": "The Basic Essentials: Statistics For Machine Learning | Towards Data Science",
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It also helps in adverstising on the website.\n\n\n  * Cookie\nedgebucket\n  * Duration\nsession\n  * Description\nReddit sets this cookie to save the information about a log-on Reddit user, for the purpose of advertisement recommendations and updating the content.\n\n\n  * Cookie\ndid\n  * Duration\n1 year\n  * Description\nArbor sets this cookie to show targeted ads to site visitors.This cookie expires after 2 months or 1 year.\n\n\nUncategorised\nOther uncategorised cookies are those that are being analysed and have not been classified into a category as yet.\nNo cookies to display.\nReject All Save My Preferences Accept All\nToggle Search[](https://towardsdatascience.com/)Toggle Mobile Navigation\n[](https://towardsdatascience.com/)\nPublish AI, ML & data-science insights to a global community of data professionals.\nSign in[Submit an Article](https://write.insightmediagroup.io)\n[Latest](https://towardsdatascience.com/latest/)[Editor's Picks](https://towardsdatascience.com/tag/editors-pick/)[Newsletter](https://towardsdatascience.com/tag/the-variable/)[ShipAI](https://towardsdatascience.com/shipai/)\n* * *\n[Write For TDS](https://towardsdatascience.com/submissions/)\n[LinkedIn](https://www.linkedin.com/company/towards-data-science/)[X](https://x.com/TDataScience)Toggle Search\n[Data Science](https://towardsdatascience.com/category/data-science/)\n# The Basic Essentials: Statistics For Machine Learning\nImproving your ability to communicate with data\n[Kurtis Pykes](https://towardsdatascience.com/author/kurtispykes/)\nMarch 31, 20227 min read\n![Photo by Justin Morgan on Unsplash](https://assets.insightmediagroup.io/media/wp-content/uploads/2022/03/0RjhzGCT4UC5HS1S7-scaled.jpg)\nPhoto by [Justin Morgan](https://unsplash.com/@justin_morgan?utm_source=medium&utm_medium=referral) on [Unsplash](https://unsplash.com?utm_source=medium&utm_medium=referral)\nKnowledge of statistics is important if you work with data. Having a firm grasp of some fundamental concepts goes a long way in your ability to effectively communicate. You'll also understand the proper methods to collect, analyze, make decisions, and effectively present results that have been discovered from data.\nIn this article, we are going to be using the Breast Cancer Wisconsin dataset from sklearn to cover some fundamental statistics concepts. It's a classification dataset with 569 observations and 30 features.\nBelow we've imported the necessary frameworks and loaded our data into memory.\ntext\n\n```\nimport pandas as pd\nimport seaborn as sns\nimport matplotlib.pyplot as plt\nfrom sklearn.datasets import load_breast_cancer\n```\n\ntext\n\n```\nX, y = load_breast_cancer(return_X_y=True, as_frame=True)\n```\n\nLearn this step by step with the interactive [AI and Data Scientist](https://roadmap.sh/ai-data-scientist) and [Computer Science](https://roadmap.sh/computer-science) roadmaps.\n## The Basics\nOnce a dataset has been built, one of the first things that should be on the back of your mind is to inspect it. The idea is to gather information on whether the data contains what you expect, but this process will also give rise to some insights that you can keep as a seed when it comes to data preprocessing.\nThe first few things to understand are the facts about the data. That means you want to have a clear idea of:\n  * **Data dimensions -** Knowing how much data you have available is important. The amount of data you have may be the deciding factor on which machine learning algorithm to use, or on whether you remove/add certain features.\n  * **Data types -** It's important to know the type of data you have available as this will influence the type of statistical tests we conduct. Also, most machine learning models can only deal with numbers so it's good to know beforehand the type of data available so that it can be converted to a suitable format for ml algorithms.\n  * **Missing data -** This comes back to knowing the data you've got available. Data can be missing for a variety of reasons but for most machine learning models, it must be dealt with (i.e. imputation or deletion) beforehand.\n\n\nLet's take a look at our data and its dimensions:\ntext\n\n```\nprint(f\"feature dimensions: {X.shape}n\ntarget dimension: {y.shape}\")\n```\n\ntext\n\n```\nX.head()\n```\n\n![Note: a portion of the table was cut so a clear screengrab could be taken; Image By Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2022/03/103QoQr8_eZqNDIInB8NECw.png)\n**Note** : a portion of the table was cut so a clear screengrab could be taken; **Image By Author**\nPandas using `None` or `NaN` to represent missing values. We can check for missing values and the data type of our features by using the `info()` method on a pandas dataframe.\ntext\n\n```\nX.info()\n```\n\n![All feature information; Image By Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2022/03/1PnAp3Z_UhVdJbaNOhILqTw.png)\n**All feature information; Image By Author**\nThe `Non-Null Count` column shows us there's no missing values in our dataset; We have 569 observations in our data and 569 values that are not null in our dataset.\n`Dtype` stands for the data type. This column tells us the data type of each feature in our dataset, which we can see are all `float64`.\n## Descriptive statistics\nThere are two types of statistics: **descriptive** and **inferential**.\nInferential statistics refers to making inferences from data, such as taking a sample to make a generalization about a population. Descriptive statistics, on the other hand, is used to better describe data.\nWhen becoming acquainted with some data, it's important to leverage descriptive statistics as this plays a major role during inference.\nSome descriptive statistical terms to be aware of are:\n### Count\nThe count is as simple as it sounds: the number of items or observations you have. Knowing the count is vital. If you wish to properly evaluate your results then you must have a good sense of how many items or observations are apparent in your data.\n### Mean\nThe mean is the average of the numbers; Calculating the mean is as simple as working out the sum of observations and diving it but the number of observations.\n![The formula for mean; Image By Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2022/03/1WMhcnAZ-houBtag3yv8mvw.png)\n**The formula for mean; Image By Author**\nIt's important because it takes into account every subject involved in the population in its calculation. But it can be a bad measurement for discovering central tendency for this same reason - i.e. outliers in a skewed distribution will have an impact on the mean.\n### Standard Deviation\nThe standard deviation measures the amount of variation of a set of values. It's calculated by taking the square root of the sum of squared differences from the mean divided by the size of the data.\n![The formula for standard deviation; x_i is each value from the population, μ is the mean, N is the size of the population, and σ is the population standard deviation; Image By Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2022/03/13Purq6v1eU9Kb79U2qi2rA.png)\n**The formula for standard deviation; x_i is each value from the population, μ is the mean, N is the size of the population, and σ is the population standard deviation; Image By Author**\nWe typically use the standard deviation in conjunction with the mean to summarize continuous data - about 95% of all values fall within two standard deviations of the mean. In a similar fashion to the mean, when the data is significantly skewed or outliers are present then the standard deviation is impacted.\n### Minimum\nThe minimum refers to the smallest value in the data set.\n### 25th Percentile\nThe 25th percentile (also called the lower quartile or first quartile) is the value under which 25% of the values in the data fall below when they are arranged.\n### Median (50th Percentile)\nThe median is the middle number of a set of values. It is the value separating the higher half from the lower half. Its purpose is to inform us of the center value of a dataset and is more useful than the mean when the data is skewed or outliers are present.\n### 75th Percentile\nThe 75th percentile (also called the upper quartile or third quartile) is the value under which 75% of the values in the data fall below when they are arranged in increasing order.\n### Maximum\nThe maximum refers to the largest value in the data set.\nLet's see how we can find this information in our dataset:\ntext\n\n```\nX.describe()\n```\n\n![Descriptive statistics about the features in our dataset; Image By Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2022/03/15kYcaCJZXYNRHyzsHaG3-Q.png)\n**Descriptive statistics about the features in our dataset; Image By Author**\nYou may also see the interquartile range being discussed in certain circles. This is in reference to the difference between the 75th percentile (Q3) and the 25th percentile (Q1).\n## Univariate analysis\nUnivariate analysis is possibly the simplest form of statistical analysis. It consists of exploring the individual features of a dataset independently of one another.\nGood information to derive from this type of analysis includes things such as the range of values, the central tendency, the skewness, and the distribution of a group. We've already covered how we can analyze the range of values (i.e. minimum, maximum, percentiles, and IQR) but we haven't spoken much about skew and distribution.\nLet's start by taking a look at the distribution of the class then we will talk about why distributions are important.\ntext\n\n```\ncounts = y.value_counts()\n```\n\ntext\n\n```\nplt.subplots(figsize=(8, 5))\nsns.barplot(x=counts.index, y=counts.values)\nplt.title(\"Distribution of target label\")\nplt.xlabel(\"Target classes\")\nplt.ylabel(\"Counts\")\nplt.show()\n```\n\n![Distribution of target label; Image By Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2022/03/1zcBiX4NpaPvsXJl13PFNsQ.png)\n**Distribution of target label; Image By Author**\nEarlier we stated that it's important to understand the data types we have available in our data since this influences our choice of statistical tests: we need to know the distribution of our data for the same reason.\nFor a classification problem, we need to know how balanced the classes are. A problem with highly imbalanced classes may require some manual handling to help our machine learning model predict the minority class better.\nLet's also take a look at the distribution of our features.\ntext\n\n```\nX.hist(figsize=(18, 16))\nplt.show()\n```\n\n![Distribution of features; Image By Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2022/03/1jOWbHdx4A4mnqnpGXeojVA.png)\n**Distribution of features; Image By Author**\nHistograms are a great way of representing the distributions of numerical data; We can discover the skewness of each feature from the image above. This tells us the measure of the asymmetry of the probability distribution about the mean - we can also learn the modality of a feature, which is the number of peaks.\nThe importance of understanding the shape of our data is high because it tells us where the most of information about our data lies. It's also important because certain models make assumptions about our data, and if our data aligned with those assumptions, it would result in better models.\nAnother way we could have learned the skew of our data is as follows:\ntext\n\n```\nX.skew()\n```\n\n![The skew of features; Image By Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2022/03/1BfPK3doBgWzYxPWTK1RY2w.png)\n**The skew of features; Image By Author**\nA skewness value of 0 means that the data is perfectly symmetrical. If the skewness is greater than 1 or less than -1 then we have highly skewed data. For features between -1 to -0.5 and 0.5 to 1, we'd say they are moderately skewed.\n## Bivariate analysis\nBivariate analysis is possible the second simplest form of statistical analysis. It refers to analyzing two variables to determine relationships between them. If there's a relationship between two variables then there will be a correlation.\nA heatmap is one way to visualize the relationships within a dataset.\ntext\n\n```\nplt.subplots(figsize=(18, 16))\nsns.heatmap(X.corr(), annot=True)\nplt.show()\n```\n\n![Image By Author](https://assets.insightmediagroup.io/media/wp-content/uploads/2022/03/1IZBZusB83FYtZIYYLeaiyQ.png)\n**Image By Author**\nWith a deeper understanding of the relationships in our data, we can gather more informative insights about our data and know to what extent it becomes easier to predict a value for one variable if we know the value of the other.\n* * *\nThis list is by no means comprehensive, but it's a good foundation to get started with. Other concepts you may want to learn about once you've grounded yourself in these ones include understanding kurtosis, hypothesis testing, and confidence intervals.\n_Thanks for reading._\nIf you enjoy reading stories like this one and wish to support my writing, consider [becoming a Medium member](https://kurtispykes.medium.com/membership). With a $5 a month commitment, you unlock unlimited access to stories on Medium. If you use [my sign-up link](https://kurtispykes.medium.com/membership), I'll receive a small commission.\nAlready a member? [Subscribe](https://kurtispykes.medium.com/subscribe) to be notified when I publish.\n> [**Get an email whenever Kurtis Pykes publishes.**](https://kurtispykes.medium.com/subscribe)\n## Register Now to Continue Reading\n### Unlock Towards Data Science with a Free Account\nAll articles on Towards Data Science are available to registered users. 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