What is the Mean?

The mean, also known as the average, is the sum of all values in a dataset divided by the number of values. It provides a measure of central tendency, representing the typical value in a dataset.

Formula:

Mean = (Sum of all values) / (Number of values)

Example in C#:

using System;
using System.Linq;
namespace StatisticsExample
{
    public class MeanExample
    {
        public static void Main(string[] args)
        {
            int[] data = { 10, 20, 30, 40, 50 };
            double mean = data.Average();
            Console.WriteLine($"Mean: {mean}");
        }
    }
}

In this example, the mean of the dataset {10, 20, 30, 40, 50} is calculated as 30.

What is the Median?

The median is the middle value in a sorted dataset. If the dataset has an even number of values, the median is the average of the two middle values. It is less sensitive to outliers than the mean.

Example:

• Dataset: {10, 20, 30, 40, 50}
• Median: 30 (middle value)
• For {10, 20, 30, 40}: Median = (20 + 30) / 2 = 25

Example in C#:

using System;
using System.Linq;
namespace StatisticsExample
{
    public class MedianExample
    {
        public static void Main(string[] args)
        {
            int[] data = { 10, 20, 30, 40, 50 };
            Array.Sort(data);
            double median =
                data.Length % 2 == 0
                    ? (data[data.Length / 2 - 1] + data[data.Length / 2]) / 2.0
                    : data[data.Length / 2];
            Console.WriteLine($"Median: {median}");
        }
    }
}

What is the Mode?

The mode is the value that appears most frequently in a dataset. A dataset can have one mode (unimodal), multiple modes (multimodal), or no mode (if all values occur with the same frequency).

Example:

• Dataset: {10, 20, 20, 30, 40}
• Mode: 20 (appears twice)

Example in C#:

using System;
using System.Collections.Generic;
using System.Linq;
namespace StatisticsExample
{
    public class ModeExample
    {
        public static void Main(string[] args)
        {
            int[] data = { 10, 20, 20, 30, 40 };
            var mode = data.GroupBy(x => x).OrderByDescending(g => g.Count()).First().Key;
            Console.WriteLine($"Mode: {mode}");
        }
    }
}

What is Variance?

Variance measures the spread of a dataset. It quantifies how much the data points deviate from the mean. A higher variance indicates more variability, while a lower variance indicates that the data points are closer to the mean.

Formula:

Variance = (Sum of squared differences from the mean) / (Number of values)

Example in C#:

using System;
using System.Linq;
namespace StatisticsExample
{
    public class VarianceExample
    {
        public static void Main(string[] args)
        {
            int[] data = { 10, 20, 30, 40, 50 };
            double mean = data.Average();
            double variance = data.Select(x => Math.Pow(x - mean, 2)).Average();
            Console.WriteLine($"Variance: {variance}");
        }
    }
}

Applications in Data Science

Understanding these statistical measures is essential for data analysis, as they help summarize data and identify patterns. Here are some examples:

• Mean: Used to calculate average sales, temperatures, or customer ratings.
• Median: Useful in income analysis to avoid distortion by extreme values.
• Mode: Commonly used in market research to identify popular products or services.
• Variance: Helps assess the consistency of manufacturing processes or investment returns.

Conclusion

Mean, median, mode, and variance are foundational concepts in statistics and data science. Mastering these measures enables data scientists to summarize datasets effectively and draw meaningful insights. Whether you are analyzing sales data, customer feedback, or experimental results, these statistical tools provide a solid foundation for understanding and interpreting data.