# Variance - definition & overview

Contents

## What is Variance and how important it is to businesses?

Variance is the deviation between a planned or standard amount and the actual result. Used to analyse and improve performance.

Variance is a term that holds a crucial place in the world of small businesses. It is a statistical measurement that depicts how data points in a specific set diverge from the average value, also known as the mean. In the context of small businesses, variance can be used to measure a wide range of factors, from financial performance to operational efficiency, and even customer satisfaction. Understanding and accurately calculating variance can provide valuable insights that can drive a small business towards success.

For small businesses, variance can be a powerful tool in decision-making processes. By understanding how different aspects of your business deviate from the average, you can identify areas of strength and weakness, and make informed decisions to improve performance. Variance can also help you anticipate and manage risk, as it provides a measure of uncertainty and volatility.

## Types of Variance

There are several types of variance that are relevant to small businesses. Each type provides different insights and is used in different contexts. Understanding these types of variance can help you make the most of this powerful statistical tool.

Firstly, there is population variance, which is used when you want to consider every possible data point in a population. This is often used in contexts where you have complete data, such as total sales over a year.

### Sample Variance

Sample variance is another type of variance that is often used in business contexts. This is used when you only have a sample of data, rather than the complete population. For example, you might use sample variance to measure customer satisfaction based on a survey of a subset of your customers.

Sample variance can provide valuable insights, but it's important to remember that it is based on a sample, not the entire population. This means that it may not accurately reflect the true variance in the entire population.

### Accounting Variance

Accounting variance is a type of variance that is specifically used in financial contexts. This measures the difference between actual financial outcomes and budgeted or forecasted outcomes. For example, if your small business budgeted for �\$10,000 in monthly sales but only achieved �\$9,000, your accounting variance would be �\$1,000.

## Calculating Variance

Calculating variance involves a specific mathematical formula. While the formula can seem complex at first glance, it becomes easier to understand with practice. The key is to break the process down into steps and tackle each one at a time.

The first step in calculating variance is to find the mean, or average, of your data set. This is done by adding up all the data points and dividing by the number of data points. Once you have the mean, you subtract each data point from the mean and square the result. This gives you a set of squared deviations. The variance is then the average of these squared deviations.

### Population Variance Calculation

When calculating population variance, you divide the sum of the squared deviations by the number of data points in the population. This gives you the average squared deviation, which is the population variance.

It's important to remember that population variance gives you a measure of how much your data points deviate from the mean on average. A high population variance means that your data points are spread out from the mean, while a low population variance means they are close to the mean.

### Sample Variance Calculation

Sample variance is calculated in a similar way to population variance, but with one key difference. Instead of dividing by the number of data points, you divide by the number of data points minus one. This is known as Bessel's correction and is used to correct for bias in the estimation of the population variance from a sample.

Like population variance, sample variance gives you a measure of how much your data points deviate from the mean on average. However, because it's based on a sample, it may not accurately reflect the true population variance.

## Importance of Variance in Small Businesses

Variance is a vital tool for small businesses. It provides a measure of uncertainty, volatility, and risk, which can be crucial in decision-making processes. By understanding variance, you can identify areas of strength and weakness in your business, make informed decisions, and manage risk effectively.

For example, if you find that your sales are highly variable from month to month, this could indicate a high level of uncertainty and risk. You might then decide to take steps to stabilise your sales, such as diversifying your product range or improving your marketing strategies.

### Variance in Financial Management

In financial management, variance is used to measure the difference between actual and budgeted outcomes. This can help you identify areas where your business is underperforming or overperforming financially.

For example, if your actual sales are consistently lower than your budgeted sales, this could indicate a problem with your sales strategy. On the other hand, if your actual costs are consistently lower than your budgeted costs, this could indicate that you are managing your resources effectively.

### Variance in Operational Efficiency

Variance can also be used to measure operational efficiency. By comparing the actual outcomes of your operations with your planned or expected outcomes, you can identify areas where your business is operating efficiently or inefficiently.

For example, if the actual time it takes to produce a product is consistently longer than the planned time, this could indicate inefficiencies in your production process. On the other hand, if the actual quality of your products is consistently higher than the expected quality, this could indicate that your production process is highly efficient.

## Limitations of Variance

While variance is a powerful tool, it's important to be aware of its limitations. One of the main limitations of variance is that it only measures the average deviation from the mean. This means that it doesn't provide information about the direction of the deviation.

For example, if you have two data points, one above the mean and one below the mean, the variance would be the same regardless of whether the point above the mean is further from the mean than the point below the mean. This can make variance less useful in contexts where the direction of the deviation is important.

### Outliers and Variance

Another limitation of variance is that it is sensitive to outliers. Outliers are data points that are significantly different from the other data points in a set. Because variance is based on the average squared deviation from the mean, a single outlier can have a large impact on the variance.

For example, if you have a data set of sales figures and one month's sales are significantly higher than the others, this could significantly increase the variance. This could give you an inflated sense of the variability in your sales, which could lead to inaccurate conclusions and decisions.

### Assumptions in Variance

Variance also makes certain assumptions that may not always hold true. For example, it assumes that your data is normally distributed, or bell-shaped. If your data is not normally distributed, the variance may not accurately reflect the variability in your data.

For example, if your sales are heavily skewed towards certain months, the variance may not accurately reflect the variability in your sales. This could lead to inaccurate conclusions and decisions.

## Conclusion

In conclusion, variance is a powerful tool that can provide valuable insights for small businesses. By understanding and accurately calculating variance, you can identify areas of strength and weakness, make informed decisions, and manage risk effectively.

However, it's important to be aware of the limitations of variance and to use it in conjunction with other statistical tools and measures. By doing so, you can make the most of variance and drive your small business towards success.