The mean and range are basic statistics often used to study past draws. The mean shows the average of the numbers drawn, while the range shows the gap between the highest and lowest numbers. These measures help illustrate how random draws can cluster or spread over time.
Histogram of Means
In lottery analysis, a histogram of means is used as a statistical tool to illustrate how often different average values of lotto combinations occur across multiple draws. This helps identify whether drawn combinations tend to produce lower, middle, or higher average numbers, giving insight into the overall balance and spread of outcomes.
The chart below is a histogram of mean values of lotto combinations from Jun. 2, 2025 to Aug. 15, 2025 , covering 75 draws. The range of possible means is divided into categories or bins. In this case, the bins are defined as intervals such as 1-5 up to 36-36, each representing a continuous range of mean values.
This division is necessary because individual mean values can vary widely, and grouping them into intervals makes patterns easier to observe. For example, by examining how frequently means fall into each bin, anyone can quickly see whether the draws are evenly distributed, clustered in particular ranges, or biased toward lower or higher averages.
The histogram of mean values reveals notable patterns. The most frequent mean range is 16-20 with 31 occurrences, suggesting this interval is the most common outcome across the draws. On the other hand, the least frequent mean range is 1-5, 26-30, 31-35, 36-36 with 0 occurrences, indicating relatively rare outcomes in this interval. This suggests a strong concentration of mean values within specific ranges. In summary, the distribution of mean values shows a tendency for draws to cluster around the higher-frequency ranges.
Histogram of Ranges
A histogram of ranges is used as a statistical representation that shows how often different spread values occur in lotto draws. It also highlights whether draws are typically made up of closely clustered numbers, broadly spread numbers, or something in between. The range of a combination is determined by subtracting the smallest number from the largest number in a draw.
The histogram of ranges below covers 75 draws from Jun. 2, 2025 to Aug. 15, 2025 . The possible range values are divided into bins or categories. In this case, the bins span intervals such as 4-7 up to 32-35, with each bin representing a continuous span of range outcomes.
This categorization is important because the range can vary significantly from draw to draw, and grouping outcomes into bins allows you to identify patterns more clearly. For instance, a concentration of draws in smaller ranges would suggest that numbers often appear close together, whereas higher frequencies in larger ranges indicate that numbers are more widely spread across the lotto field.
The histogram shows that the most frequent range is 24-27 with 26 occurrences, suggesting that combinations with this level of spread are the most common. In contrast, the least frequent range is 4-7, 8-11 with 0 occurrences, indicating that draws falling into this spread are relatively rare. This points to a clear clustering of draws around certain range values. Overall, the distribution of ranges tends to cluster in certain spread intervals, showing that draws are more likely to fall within these specific ranges.