Core Statistical Concepts for Data Science Basics AI

Explore Core Statistical Concepts for Data Science to summarize data, make inferences, and build accurate predictive models for modern analytics now.

Introduction to Statistics

When you think about Statistics, what is your first thought? You may think of information expressed numerically, such as frequencies, percentages and averages. Just looking at the TV news and the newspaper, you have seen the inflation data in the world, the number of employed and unemployed people in your country, the data about accidental incidents in the street and the percentages of votes for each political party from a survey. All these examples are statistics.

Statistics is a science concerned with developing and studying methods for collecting, interpreting and presenting empirical data. Moreover, you can divide the field of Statistics into two different sectors: 

• Descriptive Statistics 
• Inferential Statistics

The yearly census, the frequency distributions, the graphs and the numerical summaries are part of the Descriptive Statistics. 

Descriptive Statistics is considered as “The Mighty Dwarf of Data Science”

For Inferential Statistics, This refer to the set of methods that allow to generalise results based on a part of the population, called Sample.

Descriptive Statistics

As mentioned before, descriptive statistics focus on data summarization. It’s the science of processing raw data into meaningful information. Descriptive statistics can be performed with graphs, tables, or summary statistics. However, summary statistics is the most popular way to do descriptive statistics, so we would focus on this.

In the summary statistics, there are two most used: 

• Measures of Central Tendency 
• Measures of Spread.

Measures of Central Tendency

Central tendency is the center or an typical value of the data distribution or the dataset. The measures of central tendency are the activity to acquire or describe the centeral distribution of our data. The measures of central tendency would give a singular value that defines the data’s central position.

Within measures of Central Tendency, there are three popular measurements:

1. Mean 

The mean, or average, represents the sum of all values divided by the total number of observations. we use the data mean to round the data to make the data reading easier.

Mean has a disadvantage as a measure of central tendency because it is affected heavily by the outlier, which could skew the summary statistic and not best represent the actual situation. In skewed cases, we can use the median.

2. Median 

The median is the singular value positioned in the middle of the data if we sort them, representing the data’s halfway point position (50%). As a measurement of central tendency, the median is preferable when the data is skewed because it could represent the data center, as the outlier or skewed values do not strongly influence it.

3. Mode 

Mode is the highest frequency or most occurring value within the data. The data can have a single mode (unimodal), multiple modes (multimodal), or no mode at all (if there are no repeating values). 

Mode is usually used for categorical data but can be used in numerical data. For categorical data, though, it might only use the mode. This is because categorical data do not have any numerical values to calculate the mean and median.

Measures of Spread

The measures of spread (or variability, dispersion) is a measurement to describe data value spreads. The measurement provides information on how our data values vary within the dataset. It is often used with the measures of central tendency as they complement the overall data information. 

The measures of the spread also help understand how well our measures of central tendency output.

Here are various measures of spread to use. 

Range 

The range is the difference between the data’s largest (Max) and smallest value (Min). It’s the most direct measurement because the information only uses two aspects of the data.

The usage might be limited because it doesn’t tell much about the data distribution, but it might help our assumption if we have a certain threshold to use for our data.

Variance 

Variance is a measurement of spread that informs our data spreads based on the data mean.

Standard Deviation 

Standard deviation is the most common way to measure the data spread, and it’s calculated by taking the variance’s square root.

The difference between variance and the standard deviation is in the information their value gave. Variance value only indicates how spread our values were from the mean, and the variance unit differs from the original value as we squared the original values. 

However, the standard deviation value is the same unit as the original data value, which means the standard deviation value can be used directly to measure our data’s spread.

Inferential Statistics 

Inferential statistics is a branch that generalizes the population information based on the data sample it comes from. Inferential statistics is used because it is often impossible to get the whole data population, and we need to make inferential from the data sample. 

For example, we want to understand how Indonesia people’s opinions about AI. However, the study would take too long if we surveyed everyone in the Indonesian population. Hence, we use the sample data representing the population and make inferences about the Indonesian population’s opinion about AI.

Probability Distributions

A probability distribution shows the likelihood of different outcomes. Many real patterns follow common shapes, such as the normal distribution, where most values lie near the center. 

Human height works like this, with only a few very short or very tall individuals. Other distributions help explain rare events or repeated trials. These patterns make predictions easier because they show what usually happens.

Sampling

Studying a whole population takes time and money, so samples are collected instead. A good sample reflects the entire group. Random sampling reduces bias. Stratified sampling groups people into key groups to ensure no one is left out. A phone usage survey is an example. It needs people of different ages, regions, and budgets to show real trends.

Hypothesis Testing

Hypothesis testing checks if a pattern in the data is real or just random. A starting claim called the null hypothesis is tested against the sample. 

The p-value helps show how strong the evidence is. For example, a new teaching method may be tested to see if it leads to higher scores than the old method. If the difference is big, the claim of no change is rejected.

What is a p-value?

 Answer: Given that the null hypothesis is true, a p-value is the probability that you would see a result at least as extreme as the one observed.

P-values are typically calculated to determine whether the result of a statistical test is significant. In simple words, the p-value tells us whether there is enough evidence to reject the null hypothesis.

Confidence Intervals

A confidence interval gives a range where the true value is likely to fall. Instead of stating one number, the result shows a spread that reflects uncertainty. If a survey reports an average score of 75, a confidence interval might place it between 72 and 78. This range gives a clearer picture of what the real value might be.

Correlation and Covariance

Correlation shows how two variables move together. A positive correlation means they rise at the same time. A negative correlation means one rises while the other falls. Study hours and marks often rise together, which shows a positive link. Correlation helps point out relationships that may matter, but does not prove cause and effect.

Regression

Regression helps to predict one value using one or more inputs. A simple version draws a straight line through data points to show the trend. A more detailed version uses several factors at once. A store may look at price, season, and ads to predict sales. Regression is a common tool for forecasting and planning.

Data Types

Datasets contain different kinds of values. Some are numbers. Some are categories. Some follow a natural order. Each type needs the right method. Bar charts work for categories. Line charts and scatter plots suit numbers. Knowing the type helps avoid mistakes and keeps the analysis clean.

Exploratory Data Analysis

Exploratory Data analytics is the first step in any study. Charts and summaries reveal early patterns and errors. Outliers, missing values, and uneven groups become easier to spot. This stage shapes the next steps by highlighting what needs attention before any model is built.

Bias Variance Balance

Models can be simple or complicated. A simple model may miss important details. A complicated model may fit the sample too closely and fail on new data. The balance between these two sides decides how reliable the model is. This idea plays a big role in machine learning and helps create models that work beyond the training data.

Conclusion

These ideas form the foundation of statistical thinking in data science. They help make sense of messy real-world information and guide decisions in tech, business, sports, health and more. As data keeps growing, these core tools stay relevant, no matter how advanced the field becomes. But the ability to think statistically, to question, test, and reason with data will always be the skill that sets great data scientists apart.

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FAQ’s

What is the importance of descriptive statistics in data science projects?

Descriptive statistics summarize datasets using measures like mean, median, mode, range, and standard deviation for clarity.

How does sampling improve the efficiency of analyzing large populations?

Sampling studies a representative subset of a population, saving time and cost while providing accurate insights for decision-making.

Why is exploratory data analysis (EDA) considering a critical first step?

EDA identifies patterns, anomalies, missing values, and outliers, helping guide modeling and ensuring cleaner analysis.

How do correlation and regression differ in data analysis?

Correlation measures relationships between variables, while regression predicts one variable based on others, supporting forecasting.

What is the bias-variance balance, and why is it important in modeling?

Balancing bias and variance ensures models generalize well, avoiding underfitting or overfitting to produce reliable predictions.