# Random Number Histogram

• abcdmichelle
In summary, the conversation discusses how to determine if a list of 300 random numbers between 1-50 is actually random by analyzing the histogram. It is suggested that a Chi-square test can be used to determine the probability of the numbers being randomly generated. However, it is also noted that there is no way to know for sure if a given set of numbers was randomly generated.

#### abcdmichelle

1. The problem statement

If i generate a list of 300 random numbers in excel, each number between 1-50 for example, and i plot the frequency that each number comes in a histogram, how can i tell, looking at the histogram, if the numbers are really random? is there a certain distribution the histogram will follow?

## The Attempt at a Solution

I would assume that every number between 1 and 50 would have the same probability of coming up so the histogram would have more or less even bars. however, doesn't a poisson or gaussian distribution represent random events, and then wouldn't the histogram have to be a bell shaped curve?

looking at the histogram, how can i tell if the numbers are actually random?

It sounds like a Chi-square test is suitable for this. I think you use the fact that if it was random, you would expect each number 1-50 to come up 6 times, so the distribution should just be rectangular.

You can't tell by just looking. The chi-square test, as cosmo123 said, can test give a probability that numbers were generated randomly but remember it is possible (though extremely unlikely) that a randomly generated set of numbers could be all the same number! That is, there is no way of knowing for sure if a given set of numbers was randomly generated. Any set of numbers could be generated randomly.

## 1. What is a random number histogram?

A random number histogram is a graphical representation of the frequency distribution of a set of randomly generated numbers. It shows the number of occurrences of each number within a given range.

## 2. How is a random number histogram created?

A random number histogram is created by first generating a set of random numbers using a random number generator. Then, the numbers are sorted into categories or bins, and the frequency of each bin is counted. Finally, the data is plotted on a graph with the number of occurrences on the vertical axis and the number ranges on the horizontal axis.

## 3. What information can be gained from a random number histogram?

A random number histogram can provide insight into the distribution of the randomly generated numbers. It can show if the numbers are evenly distributed or if there are any patterns or biases present. It can also give an idea of the probability of certain numbers occurring.

## 4. Why is a random number histogram useful?

A random number histogram is useful for analyzing and understanding large sets of random data. It can be used in various fields such as statistics, finance, and scientific research to identify trends and patterns in data and make predictions.

## 5. Are there any limitations to using a random number histogram?

Yes, there are some limitations to using a random number histogram. It is important to ensure that the random numbers generated are truly random and not biased in any way. Additionally, the histogram may not accurately represent the distribution of the entire data set if the sample size is too small.