Statistical Measures of Central Tendency

Mahbubul Alam
Aug 19, 2020

Contents Outline

Statistical Measures of Central Tendency

Aug 19, 2020 6 minutes read


Photo by erika m on Unsplash

Introduction

In statistics, measures of central tendency are a set of “middle” values representative of the data points. Central tendency describes the distribution of data focusing on the central location around which all other data are clustered. It is the opposite of dispersion that measures how far the observations are scattered with respect to the central value.

As we will see below, central tendency is an elementary statistical concept, yet a widely used one. Among the measures of central tendency mean, median and mode are most frequently cited and used. Below we will see why they are important in the field of data science and analytics.

Figure: Conceptualizing measures of Central Tendency

1. Arithmetic Mean


Mean is the average of some data points. It is the simplest measure of central tendency that takes the sum of the observations and divides the sum by the number of observations.

In mathematical notation arithmetic mean is expressed as:

Where xi are individual observations and N is the number of observations

In a more practical example, if wages of 3 restaurant employees are $12, $14 and $15 per hour, then the average wage is $13.6 per hour. Simple as that.

Application of mean
  • We do all kinds of averages in our everyday life. We ask friends about average house rents in their neighborhoods; we calculate monthly expenses before moving to a new city. We use the arithmetic mean every day, in all contexts.
  • Businesses use means to compare the average daily sales of a product between January and February.
  • In data science, mean is an essential metric in exploratory data analysis (EDA) and is an input to all kinds of advanced modeling. Mean works behind the scene in calculating RMSE (Root Mean Squared Error), MAE (Mean Absolute Error) accuracy metrics in classification or regression algorithms.

Typology

There are a few variants of the mean. Those are not used as frequently but are useful tools in specialized use cases. Below are some examples:

Weighted meanIn ordinary mean, all data points are treated equally and equal weights are allocated (implicitly) to all data points. In weighted mean, some data are given higher (or lower) weights depending on the objectives.

Geometric meanUnlike ordinary mean, geometric mean multiplies N values and take N-th root of the product. So, for two values 2 & 8, the geometric mean would be 4.

Harmonic meanIt is another kind of mean that is calculated by taking reciprocals of data points, then taking their overage and finally taking reciprocal of the result.

Limitations of mean

Although arithmetic means is the most widely known measure of Central Tendency, it is not a robust metric; it can be highly sensitive to outliers.

Let’s consider the following two cases. On the left, the average of the four values is perfectly in the middle of the dataset. However, on the right, just one outlier data (16) changed the “center of gravity” and dragged the mean to further right. To overcome this limitation of arithmetic mean, we have another measure of central tendency — Median.

Figure: Impact of an outlier on the arithmetic mean of a dataset (illustration: author)

2. Median


What number is at the center of the list [2, 3, 4]? The answer is of course 3. And that’s the median. What if the same numbers are ordered differently, say [2, 4, 3]? Is the median now 4? No, it’s still 3. So median is the number at the center of a series after they are ordered (ascending or descending).

Let’s say we have a list of five numbers [4, 6, 2, 10, 7] and we want to find the median. The process is simple:
  1. Data: [4, 6, 2, 10, 7]
  2. Order the list: [2, 4, 6, 7, 10]
  3. Find the number at the center: 6 (median)


But what if we have even numbers in the list [4, 7, 6, 2, 10, 8]? Now there are two values in the middle, so in this case the solution is to take an average of them:
  1. Data: [4, 7, 6, 2, 10, 8]
  2. Order the list: [2, 4, 6, 7, 8, 10]
  3. Find two numbers at the center: [6, 7]
  4. Take an average: 6.5 (median)


Advantages and disadvantages of median

Why median and what’s the benefit of using it as a measure of central tendency? One big reason is, unlike mean, it’s not sensitive to extreme values. For example in the list [2, 3, 4] the last value could have been 400 instead of 4, yet the median will remain the same 3.

The other good case for median is the interpretation of data. Median splits data perfectly into two halves, so if median income in Howard County is $100,000 per year, you could simply say that half the population has higher and the remaining half has lower than $100k income in the county.

However, there is an obvious disadvantage. Median uses the position of data points rather than their values. That way some valuable information is lost and we have to rely on other kinds of measures such as measures of dispersion (next section) to get more information about the data.

Use cases

Some applications of median are well-known. Have you noticed that the US Census Bureau reports household income as “Median household income”? Or Bureau of Labor Statistics reporting wages of Americans as “Median wage”? That is because the large number of data collected through surveys or census are highly dispersed having both extremely small and large values. In such cases, median is a better measure of the center of distributions than mean is.



Figure: Average and median wages in the US. (Source: Social Security Administration; accessed: July 19, 2020)

3. Mode

In a list of numbers — say, [2, 3, 4, 4] — the most frequently occurring one is 4; that’s mode. It can apply to text data as well, for example, the mode of the set {“John”, “Kelly”, “Nadia”, “John”, “Michael”} is “John”, because it appears twice in this set of names.

A distribution can have more than one mode as in the list [2, 2, 3, 4, 4]; it’s called bimodal distribution of a discrete variable. Along this logic, a distribution with more than two modes are called multimodal distribution.

Use cases
  • Understanding mode of a distribution is important because frequently occurring values are more likely to be picked up in a random sample.
  • What’s the most frequently occurring first name in a city? Mode has the answer. Understanding mode helps with many more such problems in the field of Natural Language Processing (NLP).
  • Mode can help a grocery chain figure out which product is selling the most on different days of the week, month or year.

Summary


In summary, central tendency is an important set of concepts in statistics and data science that measures how some observations are positioned around a central value. Arithmetic mean is simply an average of datapoints, median is the value at the center of a dataset and mode returns the most frequently occurring value (numeric or text). These measures have a wide number of use cases in data science — from exploratory data analysis to measuring accuracy metrics in classification algorithms to natural language processing.

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This process uncovers hidden insights, making it a valuable endeavor in today's data-driven world.The AI RevolutionThe AI revolution has given rise to an exciting era of possibilities in unstructured data mining. AI's remarkable capabilities are instrumental in taming the unstructured data landscape, and it involves a multitude of components, including:Machine learning enables AI systems to learn from data, make predictions, and identify patterns, enhancing data mining capabilities.Deep learning uses neural networks to model complex patterns in unstructured data, which is particularly valuable in image and speech recognition.Sentiment analysis gauges emotional tones within textual data, helping to understand public opinion and tailor strategies.Pattern recognition identifies recurring structures in data, aiding in image processing and text mining.Knowledge graphs structure data relationships, improving contextual understanding and data retrieval.Anomaly detection identifies outliers in data, which is essential for fraud detection and data security.Challenges in Unstructured Data MiningAs promising as AI is at handling unstructured data, it's not without its set of challenges. Here, we delve into some of the major hurdles:Data QualityUnstructured data is inherently messy. It's laden with errors, inconsistencies, and biases, which makes it a challenge to extract meaningful insights from this data. AI systems need to be trained rigorously to navigate and decipher this diversity in data quality. Techniques like data cleansing, normalization, and the use of context are essential in ensuring that AI systems provide accurate results.ScalabilityAs the volume of unstructured data grows, AI systems must scale to handle the data influx effectively. Traditional hardware and algorithms might not be sufficient to handle this data influx. Scalable infrastructure and distributed computing become crucial to ensuring that AI systems can process and analyze vast amounts of data efficiently.Privacy ConcernsMining unstructured data often raises ethical questions regarding privacy and data protection. That’s why it’s essential to strike the right balance between data utilization and respecting individual privacy. It's a challenge to ensure that AI systems are used responsibly and in compliance with data protection laws and regulations, such as GDPR in Europe. Techniques like anonymization and consent management play a vital role in addressing these privacy concerns.Opportunities and ApplicationsAI's role in unstructured data mining has opened up a world of opportunities across various industries. Let's explore some of the most promising applications:Customer InsightsUnstructured data, particularly sourced from social media and customer reviews, serves as a goldmine of information on customer behavior and preferences. By leveraging AI algorithms, companies can analyze sentiments, spot emerging trends, and even forecast future buying patterns. With these insights, they can fine-tune their marketing strategies, product development, and customer service to align with their ever-evolving audience's demands.Healthcare DiagnosisThe abundance of unstructured data found in medical records, radiological images, and wearable device data holds the key to transformative advancements. AI-powered systems, known for their proficiency in the analysis of this data, not only facilitate early disease detection but also provide highly individualized treatment plans, ultimately raising the standard of patient care. For example: AI expedites the process of analyzing medical images for anomalies, resulting in a significant reduction in the time required for diagnosing and treating severe conditions.Fraud DetectionWhen it comes to financial institutions, AI is a vital tool for exposing fraudulent activities that often hide within the vast volumes of unstructured transaction data. Through a meticulous examination of transaction patterns and anomalies, AI systems can rapidly pinpoint fraudulent actions, providing businesses with a robust defense against significant financial losses. The ability to detect and thwart fraud in real-time provides a critical advantage, resulting in annual savings of billions of dollars for businesses.ConclusionThe future belongs to those who embrace the AI revolution in unstructured data mining. In this future, data isn't just information; it's the key to success. So, let's move forward, embracing this tomorrow, where possibilities are limitless and opportunities are endless.

Data Science
Data-Driven Creativity: Enhancing Video Content through Data Science

In the age of digital marketing and content creation, data-driven creativity is becoming an increasingly important concept. It's the fusion of artistic vision with the insights gleaned from data science to enhance the impact and effectiveness of video content. This 2500-word blog will explore how data science can be leveraged to elevate video content creation, ensuring that it not only engages but also resonates with the intended audience.Introduction to Data-Driven CreativityData-driven creativity marks a groundbreaking shift in video content creation, blending artistic vision with the insights provided by data science. This combination allows creators to break free from conventional creative limits, using data analytics to develop content that is both visually captivating and strategically significant. By delving into viewer behavior, preferences, and interactions, creators can refine their stories and visuals, achieving a deeper connection with their audience. This technique effectively transforms data into a guide for storytelling, steering content towards increased relevance and attractiveness. Consequently, video content becomes a more potent medium for engaging viewers and delivering impactful messages. Fundamentally, data-driven creativity is about converting data points into compelling stories and turning analytical insights into creative masterpieces, thereby redefining the standards of digital video content.Understanding the Role of Data in Video Content CreationExploring the Role of Data in Video Content Creation ventures into the rapidly growing realm of data-driven creativity, where data science emerges as a key instrument in enriching video content. In this realm, data transcends mere figures to become a narrative element, providing rich insights into what audiences prefer, how they behave, and emerging trends. Utilizing data, video creators can break free from conventional creative constraints, shaping their stories to more deeply connect with viewers. This process involves a detailed examination of viewer interactions, demographics, and feedback to hone storytelling skills, aiming to create videos that are not only watched but also emotionally impactful and memorable. Data-driven creativity is a fusion of art and science, where each view, reaction, and comment plays a role in directing the trajectory of video content, enhancing its relevance, engagement, and effect. This marks a transformative phase in content creation, where data equips creators to weave narratives that are not just creatively rich but also finely tuned to the dynamic preferences and interests of their audience.The Process of Gathering and Analyzing DataCollecting and analyzing data forms the foundation of data-driven creativity, especially in the realm of video content enhancement. This process involves the acquisition of key information, including audience demographics, interaction metrics, and performance measures, utilizing sophisticated tools and technologies. These range from social media analytics to advanced data mining applications designed to track a broad spectrum of viewer interactions. Once collected, this data undergoes thorough analysis to identify trends, preferences, and behaviors within the target audience. Such analysis equips content creators with insightful knowledge, allowing them to adjust their video content for greater appeal and connection with their audience. Leveraging these insights, creators can modify elements such as the tone, style, and themes of their content, revolutionizing storytelling methods and ensuring their content is both captivating and impactful. This integration of data science with creative storytelling heralds a transformative phase in video content production, where analytical findings significantly enhance artistic expression.Tailoring Content to Audience PreferencesAdapting content to audience preferences through data-driven creativity signifies a vital evolution in video content production. By incorporating data science, creators gain profound insights into audience behaviors, likes, and engagement patterns. This approach facilitates the creation of content that better resonates with viewers, ensuring everything from the plot to visual elements aligns with their interests. Utilizing analytics such as viewer habits and interaction rates, creators can pinpoint engaging aspects for better video content. Using a high-quality video editor tool is important to make the video look better. This knowledge allows precise adjustments, making the content not only captivating but also highly relevant. Ultimately, incorporating data in video content creation leads to more impactful and resonant viewer experiences, forging a deeper bond between the audience and the content.Enhancing Storytelling with Data InsightsUtilizing data insights to enhance storytelling is a groundbreaking method in video content production. Termed data-driven creativity, this technique blends the storytelling craft with data science accuracy. Content creators leverage analysis of viewer engagement, preferences, and behavior to fine-tune their narratives, ensuring a deeper connection with their audience. This integration results in not only engaging narratives but also ones that are in tune with audience interests and emerging trends. Insights from data grant a clearer understanding of what truly engages viewers, empowering creators to optimize their storytelling for the greatest effect. This modern approach reinvents traditional storytelling into an experience that's both more impactful and centered around the audience, with each creative decision being shaped and enriched by data.Using Data to Predict Future TrendsUtilizing data for future trends in data-driven creativity marks a revolutionary step in improving video content via data science. This technique focuses on analyzing viewer interactions, demographic information, and behavioral tendencies to predict future content direction. Using data enables creators to be proactive, crafting video content that resonates with emerging audience preferences and interests. Such a forward-thinking approach guarantees ongoing relevance in a dynamic digital world and fosters innovation and leadership among content creators. The blend of data analytics and artistic insight leads to the production of not just captivating but also pioneering videos, demonstrating the significant role of data in shaping the future of video content creation.Balancing Creativity and DataAchieving a harmonious blend of creativity and data in video content production is both subtle and potent. Data-driven creativity embodies the convergence of artistic flair and data analytics, providing an innovative method to boost video effectiveness. By weaving in data analysis, video creators unlock insights into what their audience prefers and how they behave, guiding their artistic choices. This integration results in content that is not only enthralling but also deeply meaningful to viewers. It is essential, however, to ensure that data serves as a guide, not a ruler, in the creative journey. This equilibrium keeps the content fresh and appealing while aligning it thoughtfully with data-driven knowledge. In essence, data-driven creativity in video content merges the narrative craft with analytical insights, culminating in videos that are both compelling and influential.Overcoming Challenges in Data-Driven CreativityOvercoming hurdles in data-driven creativity necessitates a nuanced integration of data science into the creation of video content. It involves striking a delicate balance between analytical methodologies and artistic expression, ensuring that data serves as an informative tool rather than a constraint on creativity. Accurate interpretation of data empowers content creators to avoid formulaic outputs, utilizing insights to enrich storytelling and enhance audience engagement. This intricate process demands a comprehensive understanding of the artistry of video creation and the scientific principles behind data analysis. Ethical considerations, including respecting audience privacy and obtaining data consent, are pivotal in this approach. Innovative strategies within data-driven creativity empower creators to produce content that forges deeper connections with viewers, setting new benchmarks in the digital landscape. Embracing these challenges is essential for unlocking the full potential of data-enhanced video content.Ethical Considerations in Data-Driven CreativityIn the domain of data-driven creativity, ethical considerations play a crucial role, especially when utilizing data science to enhance video content. While utilizing data insights can enhance creative processes, it is essential to address privacy concerns and ensure transparent, responsible data usage. Achieving the right equilibrium between creativity and ethical considerations becomes paramount as brands employ data to customize video content. Upholding user privacy and securing informed consent are fundamental principles in ethical data-driven creativity, fostering trust among audiences. Moreover, there is an obligation to avoid perpetuating biases and stereotypes in content creation, championing inclusivity and diversity. Ethical practices not only maintain brand integrity but also contribute to a positive and respectful digital environment for consumers.Tools and Resources for Data-Driven Video CreationExplore the potential of data-driven creativity using state-of-the-art tools and resources for crafting videos. In the current digital landscape, integrating data science and video content is transforming the landscape of creative processes. Immerse yourself in a domain where insights derived from data direct every facet of video production. These tools empower creators to customize content according to audience preferences, ensuring that each video is not only visually captivating but also strategically aligned. From scriptwriting informed by analytics to incorporating personalized visual elements, the utilization of data science takes video content to unprecedented levels. Delve into the crossroads of technology and creativity, where strategies driven by data redefine storytelling, captivating audiences in a personalized and meaningful manner.The Future of Data-Driven Creativity in Video ContentThe evolution of data-driven creativity in video content is set to transform our interaction with digital media. Through the incorporation of data science, creators gain valuable insights into viewer preferences, behavior, and trends. This collaboration enables a personalized and captivating viewing experience, heightening audience engagement. With the utilization of data-driven creativity, content producers can shape videos to suit the unique preferences of their target audience, resulting in more impactful storytelling and brand communication. As technology progresses, we anticipate a shift towards highly personalized content, driven by data insights, leading to innovative approaches in video production. This convergence of creativity and data science holds significant promise for the future development of video content within the digital landscape.ConclusionIn summary, the convergence of data-driven insights and creative components represents a transformative shift in the realm of video content creation. The fusion of Data Science and creativity provides content producers with the tools to precisely tailor videos to audience preferences, resulting in more impactful and engaging content. Leveraging the potential of data facilitates a deeper comprehension of viewer behavior, enabling targeted storytelling. Amidst the digital landscape, the symbiosis of data and creativity not only elevates video content but also fosters innovation and personalized experiences. Looking ahead, embracing Data-Driven Creativity becomes crucial for maintaining a leading edge in the continually evolving landscape of video content creation.

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