In data analysis and statistics, it is common to encounter the need to calculate various types of averages. The three most widely used types of averages are mean, median, and mode. These averages provide valuable insights into the data and help in making informed decisions. In this article, we will explore these statistical functions and learn how to calculate them using SQL Server.

Mean

The mean, also known as the average, is calculated by summing up all the data points in a series and dividing the sum by the total number of data points. The formula for calculating the mean is:

Mean = (Sum of all data points) / (Total number of data points)

For example, let’s calculate the mean of a series: 2, 8, 4, 6, 2, 2. The sum of these values is 24, and since there are 6 data points, the mean is calculated as 24/6 = 4. Therefore, the mean of the series is 4.

Median

The median is the middle value in a series when the data points are arranged in ascending order. If there are an even number of data points, the median is calculated as the average of the two middle values. To calculate the median:

1. Arrange the data points in ascending order.
2. If the number of data points is odd, the median is the middle value.
3. If the number of data points is even, the median is the average of the two middle values.

For example, let’s consider the series: 2, 8, 4, 6, 2, 2. When arranged in ascending order, the series becomes: 2, 2, 2, 4, 6, 8. Since there are 6 data points (an even number), the two middle values are 2 and 4. Therefore, the median is calculated as (2 + 4) / 2 = 3.

Mode

The mode is the value that appears most frequently in a series. It represents the most common number in the dataset. There is no specific formula to calculate the mode, as it simply considers the highest frequency in the series.

For example, let’s consider the series again: 2, 8, 4, 6, 2, 2. In this series, the number 2 appears three times, while all the other numbers appear only once. Therefore, the mode for this series is 2.

Calculations in SQL Server

In SQL Server, we can easily calculate these statistical functions using SQL queries. Let’s use the same series mentioned earlier and demonstrate how to calculate the mean, median, and mode using SQL.

CREATE TABLE #TempStats(
    [Number] INT
)

INSERT INTO #TempStats ([Number])
VALUES (2),(8),(4),(6),(2),(2)

-- Mean
SELECT AVG([Number]) AS [Mean] FROM #TempStats

-- Median
SELECT (
    (
        SELECT TOP 1 [Number] FROM (
            SELECT TOP 50 PERCENT [Number]
            FROM #TempStats
            WHERE [Number] IS NOT NULL
            ORDER BY [Number] ASC
        ) FirstHalf
    ORDER BY [Number] DESC
    )
    +
    (
        SELECT TOP 1 [Number] FROM (
            SELECT TOP 50 PERCENT [Number]
            FROM #TempStats
            WHERE [Number] IS NOT NULL
            ORDER BY [Number] DESC
        ) SecondHalf
        ORDER BY [Number] ASC
    )
) / 2 AS [Median]

-- Mode
SELECT TOP 1 [Number] [Mode]
FROM #TempStats
WHERE [Number] IS NOT NULL
GROUP BY [Number]
ORDER BY COUNT(1) DESC

DROP TABLE #TempStats

Conclusion

In this article, we have explored the basics of statistical functions – mean, median, and mode – and learned how to calculate them using SQL Server. These functions are essential in data analysis and provide valuable insights into the data. By understanding and utilizing these functions, you can make informed decisions based on the data at hand.