# Importance of standard deviation and mean relationship

This is the main reason why sample size is such an important factor in intervention Maybe there is some confusion with the "standard error of the mean" (SEM)? If you . Does how large or small the standard deviation is have any relation to. What is the relationship between standard deviation and mean? 3, Views · What is difference What is the importance of standard deviation? 1, Views. Learn about the difference between the standard error of the mean and However, the meaning of SEM includes statistical inference based on.

### What is Standard Deviation and how is it important?

Weather[ change change source ] As a simple example, consider the average daily high temperatures for two cities, one inland and one near the ocean. It is helpful to understand that the range of daily high temperatures for cities near the ocean is smaller than for cities inland. These two cities may each have the same average daily high temperature. However, the standard deviation of the daily high temperature for the coastal city will be less than that of the inland city.

### Standard deviation - Simple English Wikipedia, the free encyclopedia

Sports[ change change source ] Another way of seeing it is to consider sports teams. In any sport, there will be teams that are good at some things and not at others.

The teams that are ranked highest will not show a lot of differences in abilities. They do well in most categories.

The lower the standard deviation of their ability in each category, the more balanced and consistent they are. Teams with a higher standard deviation, however, will be less predictable.

## Standard deviation

A team that is usually bad in most categories will have a low standard deviation. A team that is usually good in most categories will also have a low standard deviation. However, a team with a high standard deviation might be the type of team that scores many points strong offense but also lets the other team score many points weak defense. Trying to know ahead of time which teams will win may include looking at the standard deviations of the various team "statistics.

In racingthe time a driver takes to finish each lap around the track is measured. A driver with a low standard deviation of lap times is more consistent than a driver with a higher standard deviation. This information can be used to help understand how a driver can reduce the time to finish a lap. Money[ change change source ] In money, standard deviation may mean the risk that a price will go up or down stocks, bonds, property, etc.

It can also mean the risk that a group of prices will go up or down [3] actively managed mutual funds, index mutual funds, or ETFs. Risk is one reason to make decisions about what to buy. Risk is a number people can use to know how much money they may earn or lose. But now the life is not that easy, Managers understand Risk. They dont like to invest in shares that go up and down everybody wants a stable life! Business Consideration Average return or for that matter any averagenever tells you the full story.

It gives you the central value of data, but does not tell you about the spread. So we need to measure spread which is akin to risk!

If I were to ask you the simplest measure of spread, what would pop in your mind? I would say that the simplest measure is Range [Min, Max]. It gives me a fair idea of spread. But it again gives me only half of the story.

The Minimum and Maximum might be skewed. It would be the same for data sets that are uniform, but have an extreme min and max and same for skewed data around min and max. Excel gives simple functions to calculate Range. Measuring Spread Using Standard Deviation Just like Range gave us the simple measure of spread by telling us the Min and Max values of data, we have another measure called standard deviation or an equivalent measure called variance to measure spread.

Standard Deviation essentially Measures the spread Differences of individual data points from the mean Squares the differences So that positives and negatives all become positive Takes the average of these squared differences Excel makes your life easier.

Just use the function, StdevP or VarP and show it the data. It does all the number crunching on its own!

## Standard Deviation and Variance (1 of 2)

It measures the deviation from the mean, which is a very important statistic Shows the central tendency It squares and makes the negative numbers Positive The square of small numbers is smaller Contraction effect and large numbers larger Expanding effect. So it makes you ignore small deviations and see the larger one clearly! The square is a nice function!

- What is Standard Deviation?