Contents

We often hear people talk about the mean and variance of a data set, but what do these terms actually mean? In this blog post, we’ll take a look at what the mean and variance represent and how to calculate them in JavaScript.

Checkout this video:

## Introduction

In statistics, the mean is the sum of all the values in a data set divided by the number of values in the set. The variance is the sum of the squares of all the values in a data set divided by the number of values in the set. In JavaScript, you can use the built-in mean and variance functions to calculate these values for an array of numbers.

The mean and variance are important values to know when working with data sets because they give you a measure of how spread out the data is. The mean is sometimes called the average, but it’s important to note that not all data sets have an average value. The variance is a measure of how far each value in a data set is from the mean.

To calculate the mean and variance for a data set, you first need to have an array of numbers. You can create an array in JavaScript with the following code:

var numbers = [1,2,3,4,5];

Once you have your array of numbers, you can use the built-in mean and variance functions to calculate those values. To calculate the mean, you would use the following code:

var average = numbers.mean();

To calculate the variance, you would use this code:

var variance = numbers.variance();

Both of these functions will return a single number that represents either the mean or variance of your data set.

## What is Mean?

Mean is a simple mathematical concept that is used to calculate the average value of a set of data. The mean is calculated by adding up all the values in a set of data and then dividing by the number of values in the set.

### Arithmetic Mean

The arithmetic mean is the most common type of mean, and is simply the sum of all values divided by the number of values. So, in our example above, the arithmetic mean of 1, 2, 3, 4 and 5 is:

(1 + 2 + 3 + 4 + 5) / 5 = 15 / 5 = 3

You can see that the arithmetic mean is just the average of all the values.

### Geometric Mean

The geometric mean is a type of mean that is typically used to find the average growth rate over a period of time. To calculate the geometric mean, you take the nth root of the product of n numbers. For example, if you wanted to find the average growth rate for a stock over 5 years, you would take the 5th root of the product of 5 numbers.

### Harmonic Mean

The harmonic mean is the reciprocal of the arithmetic mean of the reciprocals. In other words, it is the arithmetic mean of the reciprocals of a set of numbers. The harmonic mean is often used when averaging rates, such as speeds. For example, the harmonic mean of 1 mph and 100 mph would be 2/(1/1 + 1/100) = 50 mph.

## What is Variance?

In statistics, variance is a measure of how spread out data is. It is the average of the squared differences from the mean. So, if we have two data points, (1,2) and (3,4), the variance would be:

### Population Variance

The population variance is a measure of how spread out the values in a population are. It is calculated by taking the sum of the squared differences between each value and the population mean, and then dividing that sum by the number of values in the population.

The population variance can be a useful quantity when trying to understand how spread out a population is, but it can be difficult to interpret because it is in units that are squared (e.g. if the population mean is 5 and the population variance is 2, then the difference between 5 and any other value will be squared).

A related quantity that is often used instead of the population variance is the standard deviation, which is simply the square root of the variance. The standard deviation has the same units as the original values, which makes it easier to interpret.

### Sample Variance

In statistics, the variance is a measurement of how far a set of numbers is spread out. It measures the average degree to which each number in the set differs from the mean. The variance is calculated by taking the difference between each number in the set and the mean, and then squaring and taking the average of those numbers.

For example, let’s say we have a set of five numbers: 1, 2, 3, 4, and 5. The mean of this set is 3. To calculate the variance, we take each number in the set and subtract 3 from it. So for 1, that’s -2; for 2, that’s -1; for 3, that’s 0; for 4, that’s 1; and for 5, that’s 2:

1: -2

2: -1

3: 0

4: 1

5: 2

Then we square each of those numbers (-2 squared is 4; -1 squared is 1; 0 squared is 0; 1 squared is 1; and 2 squared is 4):

1: 4

2: 1

3: 0

4: 1

5: 4

And finally we take the average of those numbers (4 + 1 + 0 + 1 + 4 = 10 divided by 5 = 2):

variance = 2

## Conclusion

In conclusion, mean and variance can tell us a lot about a data set in JavaScript. They can be used to find trends, spot outliers, and calculate standard deviation. Just remember to use the correct form of each statistic when working with your data!