# What Is Variation?

- The Human Factor
- The 3sigma-model and the distance to a standard
- The height of a sunflower
- Variation from the average or mean in statistics
- ANOVA: a new approach to group variance analysis
- The Coefficients of Variation for the Mean and Average
- The spread of data
- Margin Call for Derivative Contracts
- Coefficients of variation in finance
- A Percent Variance Theorem
- Calculating Variation in Customer Satisfaction
- The Interquartile Range

### The Human Factor

All people are human. They are both from the same species. Your friends and classmates may have different hair and eye colors.

### The 3sigma-model and the distance to a standard

The reason for using 3sigma is that 99% of the data of a variable will be found at a distance from the average.

### The height of a sunflower

The weight of a dog is caused by its genes, environmental and heredity. The height of a sunflowers is determined by how much light and water it gets.

### Variation from the average or mean in statistics

Variation from the average or mean is measured in statistics. It is calculated by taking the differences between the numbers and the mean and then squaring them to make them positive, and finally dividing the squares by the number of values in the data set. Statisticians use variance to see how individual numbers relate to each other in a data set, rather than using broader mathematical techniques such as arranging numbers into quartiles.

### ANOVA: a new approach to group variance analysis

The main idea behind an ANOVA is to compare the variances between groups and groups within groups to see if the results are best explained by the group differences or individual differences.

### The Coefficients of Variation for the Mean and Average

The mean of the population is compared to the coefficients of variation for the data. The amount of return expected from investments is compared to the amount of risk assumed by investors in finance. The better the risk-return trade-off is, the lower the standard deviation to mean return should be.

### The spread of data

The data is more scattered from its mean if the value of variance is low or minimum. It is a measure of the spread of data.

### Margin Call for Derivative Contracts

The minimum amount of funds that must be maintained in the trading account is called maintenance margin. The maintenance margin is important for both parties to keep their trading account solvent. There is news in the market that a future contract for 50 kilograms of Apple is currently trading at 500.

The market is volatile and can affect the buyer of the contract. The initial margin is the amount of money that will be deposited into the contract. The amount can be set in percentages or in absolute numbers.

The variation margin is only paid when the balance of the trading account is below the maintenance margin. There is a level of safety between the initial margin and the maintenance margin. There is no obligation to pay any margin if the balance is between the initial margin and maintenance margin.

The trader has top the initial margin if the balance is below the maintenance margin. The margin balance is the amount of money in the account. When the margin balance reaches below the maintenance margin or the derivative, a margin call is made.

The variation margin is used as a security for successful execution of the derivative contract. It helps to protect the interest of the party that enters into the contract. The trading account balance is assessed daily after accounting for market fluctuations.

### Coefficients of variation in finance

The coefficients of variation are important in finance. The financial metric shows the risk-to-reward ratio of an investment and the mean of the reward.

### A Percent Variance Theorem

A percent variance is the change in an account during a period of time from one period to the next expressed as a ratio. It shows the increase or decrease in an account over time as a percentage of the total account value.

### Calculating Variation in Customer Satisfaction

Variation is one of the summary statistics. It is used to represent the amount of dispersion in the data set. It helps to understand how values are spread.

The central tendency of the data set is what determines how close or far each value is. The measure of central tendency is relevant, but variation has more impact on the end customers. If the child scores way below average, the parent will not care about the average score.

If your pizza arrives after 40 minutes, you will not care about delivery time. Customer satisfaction will be higher for process A as it varies less than process. B.

The specification limits are higher than the process. B. The range is higher for process B than for process A.

Range is fairly easy to understand calculate, but it doesn't give much information about the data set or the variation within. It doesn't show tightly the data is clustered around the center since range depends on the extreme values. It is very prone to be influenced by outliers since range depends on two extreme values.

### The Interquartile Range

The interquartile range uses only 2 values in its calculation. The 2 values that come from the middle half of the data set are unlikely to be extreme scores. Population data can give you an exact value for population standard deviation. The standard deviation is the amount of variability in your distribution.

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