7 Key Statistics Concepts Every Data Scientist Must Master

BY BALA PRIYA CPOSTED ON AUGUST 9, 2024

Statistics is one of the must-have skills for all data scientists. But learning statistics can be quite the task.

That’s why we put together this guide to help you understand essential statistics concepts for data science. This should give you an overview of the statistics you need to know as a data scientist and explore further on specific topics.

Let’s get started.

1. Descriptive Statistics

Descriptive statistics provide a summary of the main features of a dataset for preliminary data analysis. Key metrics include measures of central tendency, dispersion, and shape.

Measures of Central Tendency

These metrics describe the center or typical value of a dataset:

• Mean: Average value, sensitive to outliers
• Median: Middle value, robust to outliers
• Mode: Most frequent value, indicating common patterns

Measures of Dispersion

These metrics describe data spread or variability:

• Range: Difference between highest and lowest values, sensitive to outliers
• Variance: Average squared deviation from the mean, indicating overall data spread.
• Standard deviation: Square root of variance, in the same unit as the data. Low values indicate data points close to the mean, high values indicate widespread data.

Measures of Shape

These metrics describe the data distribution shape:

• Skewness: Asymmetry of the distribution; Positive for right-skewed, negative for left-skewed
• Kurtosis: “Tailedness” of the distribution; High values indicate heavy tails (outliers), low values indicate light tails

Understanding these metrics is foundational for further statistical analysis and modeling, helping to characterize the distribution, spread, and central tendencies of your data.

2. Sampling Methods

You need to understand sampling for estimating population characteristics. When sampling, you should ensure that these samples accurately reflect the population. Let's go over the common sampling methods.

Random Sampling

Random sampling minimizes bias, ensuring the samples are representative enough. In this, you assign unique numbers to population members and use a random number generator to select the samples at random.

Stratified Sampling

Ensures representation of all subgroups. Stratified sampling divides population into homogeneous strata(such as age, gender) and randomly samples from each stratum proportional to its size.

Cluster Sampling

Cluster sampling is cost-effective for large, spread-out populations. In this, divide population into clusters (such as geographical areas), randomly select clusters, and sample all or randomly select members within chosen clusters.

Systematic Sampling

Systematic sampling is another technique that ensures evenly spread samples.
You assign unique numbers, determine sampling interval (k), randomly select a starting point, and select every k-th member.
Choosing the right sampling method ensures the design effectiveness of study and more representative samples. This in turn improves the reliability of conclusions.

2. Probability Distributions

Probability distributions represent the likelihood of different outcomes. When you’re starting out, you should learn about the normal, binomial, poisson, and exponential distributions—each with its properties and applications.

Normal Distribution

Many real-world distributions follow normal distribution which has the following properties:

Symmetric around the mean, with mean, median, and mode being equal. The normal distribution is characterized by mean (µ) and standard deviation (σ).
As an empirical rule, ~68% of data within one standard deviation, ~95% within two, and ~99.7% within three.
It’s also important to talk about Central Limit Theorem (CLT) when talking about normal distributions. In simple terms, the CLT states that with a large enough sample size, the sampling distribution of the sample mean approximates a normal distribution.

Binomial Distribution

Binomial distribution is used to model the expected number of successes in n independent Bernoulli trials. Each binomial trial has only two possible outcomes: success or failure. The binomial distribution is:

Defined by the probability of success (p)
Suitable for binary outcomes like yes/no or success/failure
Poisson Distribution
Poisson distribution is generally used to model the number of events occurring within a fixed interval of time. It’s especially suited for rare events and has the following properties:

Events are independent and have a fixed average rate (λ) of occurrence
Useful for counting events over continuous domains (time, area, volume)

Exponential Distribution

The exponential distribution is continuous and is used to model the time between events in a Poisson process.
The exponential distribution is:
Characterized by the rate parameter (λ) (which is the inverse of the mean)
Memoryless, meaning the probability of an event occurring in the future is independent of the past
Understanding these distributions helps in modeling various types of data.