# Basic Statistics for Computer Engineering

Statistics play an essential role in computer engineering, providing a framework for making decisions based on data. From performance analysis to algorithm optimization and prediction modeling, the applications of statistics in computer engineering are vast.

Understanding Variables and Data Types

Data in computer engineering can be divided into different types or ‘variables’. These include:

1. Numerical Variables: These are quantitative data that exist on an ordinal scale. They can be further classified into discrete and continuous variables. For instance, the number of users online at a given time is a discrete variable, whereas the time a user spends on a webpage is a continuous variable.
2. Categorical Variables: These are qualitative data that can be divided into different categories or groups. For example, the type of browser (Chrome, Firefox, Safari, etc.) a user uses to access a webpage is a categorical variable.

Measures of Central Tendency

The measure of central tendency gives a single value that attempts to describe a set of data by identifying the central position within that set of data. The three most common measures of central tendency are:

1. Mean: It is the average value of the data set and is calculated by adding all data points and then dividing the sum by the number of data points.
2. Median: It is the middle value of the data set when sorted in ascending or descending order.
3. Mode: It is the most frequently occurring value in the data set.

Measures of Dispersion

The measure of dispersion shows how spread out the values in a data set are. This is especially important in computer engineering when studying the variability in a system’s performance. The common measures of dispersion are:

1. Range: It is the difference between the highest and the lowest values in the data set.
2. Variance: It measures how spread out the members of the data set are from the mean.
3. Standard Deviation: It is the square root of variance and provides a measure of the amount of variation or dispersion of a set of values.

Probability Distributions

Understanding probability distributions is critical for modeling the behavior of systems in computer engineering. The two main types of probability distributions are:

1. Discrete Probability Distributions: The probabilities of discrete random variables, such as the binomial distribution and Poisson distribution.
2. Continuous Probability Distributions: The probabilities of continuous random variables, such as the normal distribution and exponential distribution.

Hypothesis Testing

Hypothesis testing is a statistical method used to make inferences or draw conclusions about a population based on a sample of data. This method is essential in computer engineering for decision making, such as choosing between different algorithms or optimizing system performance.

Correlation and Regression

Correlation is a statistical measure that indicates the extent to which two or more variables fluctuate together. Regression analysis, on the other hand, is a set of statistical processes for estimating the relationships among variables. These techniques are crucial in computer engineering for studying relationships between different system variables and making predictions.

Understanding these statistical concepts is crucial for computer engineers. These tools allow engineers to analyze data effectively, make predictions, optimize performance, and make informed decisions based on data.

## Examples

Understanding Variables and Data Types

1. Numerical Variables:
• Discrete Variable Example: The number of requests a server receives each minute.
• Continuous Variable Example: The time it takes for a computer to complete a task or processing time.
2. Categorical Variables:
• Example: The operating system (Windows, Linux, macOS) on a user’s computer.

Measures of Central Tendency

1. Mean: If a server received request loads of 100, 120, 110, and 90 over four separate minutes, the mean load would be (100+120+110+90) / 4 = 105 requests per minute.
2. Median: If a set of processing times in milliseconds is {10, 15, 12, 11, 14}, the median time would be 12 milliseconds.
3. Mode: If we have data on the most-used programming languages in a certain company and the data set is {“Python”, “Java”, “C++”, “Java”, “Python”, “Python”, “C#”, “Python”}, the mode would be “Python” as it appears most frequently.

Measures of Dispersion

1. Range: For the same processing times as above {10, 15, 12, 11, 14}, the range would be 15 – 10 = 5 milliseconds.
2. Variance: If the system uptime (in hours) for a computer over five days is {23, 24, 22, 23, 24}, the mean is 23.2, and the variance is the average of the squared differences from the Mean, which is 0.16.
3. Standard Deviation: Using the uptime data from above, the standard deviation would be the square root of the variance, so approximately 0.4.

Probability Distributions

1. Discrete Probability Distributions:
• Binomial Distribution Example: The probability of a packet being lost (success) in a network can be modeled as a binomial distribution. Suppose each packet has a 1% chance of being lost, and we send 100 packets. We can use the binomial distribution to find the probability of losing exactly 5 packets.
• Poisson Distribution Example: If a server receives an average of 10 requests per minute, the number of requests received in a given minute can be modeled with a Poisson distribution.
2. Continuous Probability Distributions:
• Normal Distribution Example: The processing time of a task in a computer often follows a normal distribution, where most tasks take about the average time, and tasks that take a lot shorter or longer are less common.
• Exponential Distribution Example: The time between requests to a server might follow an exponential distribution if the requests are arriving at a constant average rate.

Hypothesis Testing

Example: An engineer wants to know if a new algorithm improves the speed of data processing. She runs the old algorithm on a set of data and measures the processing time. Then she does the same with the new algorithm. By conducting a hypothesis test, she can determine whether any observed difference in processing times is statistically significant or if it’s likely due to random chance.

Correlation and Regression

Example: A computer engineer might look at the relationship between CPU usage and system load. Through correlation, the engineer could quantify how much those two variables move together. With regression, the engineer could create a model to predict system load based on CPU usage.