Definition: A cost variance is the difference between the actual expenses incurred and the standard expenses estimated at the beginning of a period. Management uses these variances are used to analyze and track the progress of production processes, budgets, and other operations.
The variance is a way of measuring the typical squared distance from the mean and isn't in the same units as the original data. Both the standard deviation and variance measure variation in the data, but the standard deviation is easier to interpret. The red population has mean 100 and variance 100 (SD=10) while the blue population has mean 100 and variance 2500 (SD=50). In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its mean.
- No data can be judged as good or bad on the basic of its variance. Variance is a measure of heterogeneity in a given data. Higher the variance, more heterogeneous is it and smaller the variance, more homogeneous is it.
- My understanding of high variance is that the targets are spread widely around. The output values are 'all over the place'. In a binary classification model, there can only be 2 outcomes. I am at a loss when visualizing what high variance mean in a binary classification model.
What Does Cost Variance Mean?
Before a cost variance can be calculated, the standard cost must be established. This is the estimated expense that management anticipates incurring during the period. These costs usually include direct materials, direct labor, and factory overhead. When management has finishes setting their standard costs for the period, the production process can begin.
At the end of the accounting period, management analyzes the difference between the actual amount of expenses incurred and the standards that were set at the beginning. The difference between these two numbers is considered the cost variance. Variances can be favorable or unfavorable.
Example
A favorable variance occurs when the actual costs incurred are less than the estimated costs. Similar to the budgeting process, unfavorable variances occur when the actual costs are higher than the estimated expenses.
After management has identified the favorable and unfavorable variances, they can break them down into their components. Each cost variance is made up of a quantity component and a price component. Each of these components in turn have an actual amount and standard amount associated with them just like the variance. Here are the cost variance equations.
My b casino. Cost variance = Actual cost – Standard cost
Actual cost = Actual quantity x Actual price
Standard cost = Standard quantity x standard price
Management can use these formulas to analyze what happened during the accounting period and how to adjust the production process in the future. For instance, these formulas can be combined to find the price and quantity variance for the period. This way management can understand what caused the overall cost variance. Was it the change in quantities purchased, the change in price, or a combination of the two?
Contents Golden empire casino.
Deviation just means how far from the normal
Standard Deviation
The Standard Deviation is a measure of how spread out numbers are.
Its symbol is σ (the greek letter sigma)
The formula is easy: it is the square root of the Variance. So now you ask, 'What is the Variance?'
Variance
The Variance is defined as:
The average of the squared differences from the Mean.
To calculate the variance follow these steps:
- Work out the Mean (the simple average of the numbers)
- Then for each number: subtract the Mean and square the result (the squared difference).
- Then work out the average of those squared differences. (Why Square?)
Example
You and your friends have just measured the heights of your dogs (in millimeters):
The heights (at the shoulders) are: 600mm, 470mm, 170mm, 430mm and 300mm.
Find out the Mean, the Variance, and the Standard Deviation.
Your first step is to find the Mean:
Answer:
| Mean | = | 600 + 470 + 170 + 430 + 3005 |
| = | 19705 | |
| = | 394 |
so the mean (average) height is 394 mm. Let's plot this on the chart:
Now we calculate each dog's difference from the Mean:
To calculate the Variance, take each difference, square it, and then average the result:
| Variance | ||
| σ2 | = | 2062 + 762 + (−224)2 + 362 + (−94)25 |
| = | 42436 + 5776 + 50176 + 1296 + 88365 | |
| = | 1085205 | |
| = | 21704 |
High Variance D20
So the Variance is 21,704
And the Standard Deviation is just the square root of Variance, so:
| Standard Deviation | ||
| σ | = | √21704 |
| = | 147.32.. | |
| = | 147(to the nearest mm) |
And the good thing about the Standard Deviation is that it is useful. Now we can show which heights are within one Standard Deviation (147mm) of the Mean:
So, using the Standard Deviation we have a 'standard' way of knowing what is normal, and what is extra large or extra small.
Rottweilers are tall dogs. And Dachshunds are a bit short, right?
Using
We can expect about 68% of values to be within plus-or-minus1 standard deviation.
Read Standard Normal Distribution to learn more.
Also try the Standard Deviation Calculator.
But .. there is a small change with Sample Data
Sample Variance Calculator
Our example has been for a Population (the 5 dogs are the only dogs we are interested in).
But if the data is a Sample (a selection taken from a bigger Population), then the calculation changes!
What Does A High Variance Mean In Statistics
When you have 'N' data values that are:
- The Population: divide by N when calculating Variance (like we did)
- A Sample: divide by N-1 when calculating Variance
All other calculations stay the same, including how we calculated the mean.
Example: if our 5 dogs are just a sample of a bigger population of dogs, we divide by 4 instead of 5 like this:
Think of it as a 'correction' when your data is only a sample.
Formulas
Here are the two formulas, explained at Standard Deviation Formulas if you want to know more:
|
| The 'Sample Standard Deviation': |
Looks complicated, but the important change is to
divide by N-1 (instead of N) when calculating a Sample Variance.
*Footnote: Why square the differences?
If we just add up the differences from the mean .. the negatives cancel the positives:
| 4 + 4 − 4 − 44 = 0 |
So that won't work. How about we use absolute values?
| |4| + |4| + |−4| + |−4|4 = 4 + 4 + 4 + 44 = 4 |
Jack and the beanstalk casino. That looks good (and is the Mean Deviation), but what about this case:
| |7| + |1| + |−6| + |−2|4 = 7 + 1 + 6 + 24 = 4 |
Oh No! It also gives a value of 4, Even though the differences are more spread out.
So let us try squaring each difference (and taking the square root at the end):
| √(42 + 42 + (-4)2 + (-4)24) = √(644) = 4 |
| √(72 + 12 + (-6)2 + (-2)24) = √(904) = 4.74.. |
That is nice! The Standard Deviation is bigger when the differences are more spread out .. just what we want.
In fact this method is a similar idea to distance between points, just applied in a different way.
And it is easier to use algebra on squares and square roots than absolute values, which makes the standard deviation easy to use in other areas of mathematics.
