What is the significance of standard deviation

This median separates the third and fourth quartiles. This is the Interquartile range, or IQR. If there is an even number of values, then the position of the median will be in between two numbers. In that case, take the average of the two numbers that the median is between. Example: 1, 3, 7, This median separates the first and second quartiles. Thus, it is often preferred to the total range. The IQR is used to build box plots, which are simple graphical representations of a probability distribution.

A box plot separates the quartiles of the data. All outliers are displayed as regular points on the graph. The vertical line in the box indicates the location of the median of the data. The box starts at the lower quartile and ends at the upper quartile, so the difference, or length of the boxplot, is the IQR. Interquartile Range : The IQR is used to build box plots, which are simple graphical representations of a probability distribution. In a boxplot, if the median Q2 vertical line is in the center of the box, the distribution is symmetrical.

If the median is to the left of the data such as in the graph above , then the distribution is considered to be skewed right because there is more data on the right side of the median. Similarly, if the median is on the right side of the box, the distribution is skewed left because there is more data on the left side. To calculate whether something is truly an outlier or not you use the formula 1. Once you get that number, the range that includes numbers that are not outliers is [Q1 — 1.

Anything lying outside those numbers are true outliers. Variability for qualitative data is measured in terms of how often observations differ from one another. The study of statistics generally places considerable focus upon the distribution and measure of variability of quantitative variables.

A discussion of the variability of qualitative—or categorical— data can sometimes be absent. In such a discussion, we would consider the variability of qualitative data in terms of unlikeability. Unlikeability can be defined as the frequency with which observations differ from one another.

Consider this in contrast to the variability of quantitative data, which ican be defined as the extent to which the values differ from the mean. Instead, we should focus on the unlikeability. In qualitative research, two responses differ if they are in different categories and are the same if they are in the same category.

An index of qualitative variation IQV is a measure of statistical dispersion in nominal distributions—or those dealing with qualitative data. The following standardization properties are required to be satisfied:. In particular, the value of these standardized indices does not depend on the number of categories or number of samples. For any index, the closer to uniform the distribution, the larger the variance, and the larger the differences in frequencies across categories, the smaller the variance.

The variation ratio is a simple measure of statistical dispersion in nominal distributions. It is the simplest measure of qualitative variation. It is defined as the proportion of cases which are not the mode:. Just as with the range or standard deviation, the larger the variation ratio, the more differentiated or dispersed the data are; and the smaller the variation ratio, the more concentrated and similar the data are.

Descriptive statistics can be manipulated in many ways that can be misleading, including the changing of scale and statistical bias. Descriptive statistics can be manipulated in many ways that can be misleading. Effects of Changing Scale : In this graph, the earnings scale is greater. Effects of Changing Scale : This is a graph plotting yearly earnings. Both graphs plot the years , , and along the x-axis. Bias is another common distortion in the field of descriptive statistics.

A statistic is biased if it is calculated in such a way that is systematically different from the population parameter of interest. The following are examples of statistical bias.

Descriptive statistics is a powerful form of research because it collects and summarizes vast amounts of data and information in a manageable and organized manner. Moreover, it establishes the standard deviation and can lay the groundwork for more complex statistical analysis. In other words, every time you try to describe a large set of observations with a single descriptive statistics indicator, you run the risk of distorting the original data or losing important detail.

Exploratory data analysis is an approach to analyzing data sets in order to summarize their main characteristics, often with visual methods. Exploratory data analysis EDA is an approach to analyzing data sets in order to summarize their main characteristics, often with visual methods.

It is a statistical practice concerned with among other things :. Primarily, EDA is for seeing what the data can tell us beyond the formal modeling or hypothesis testing task. EDA is different from initial data analysis IDA , which focuses more narrowly on checking assumptions required for model fitting and hypothesis testing, handling missing values, and making transformations of variables as needed.

Exploratory data analysis was promoted by John Tukey to encourage statisticians to explore the data and possibly formulate hypotheses that could lead to new data collection and experiments. Both of these try to reduce the sensitivity of statistical inferences to errors in formulating statistical models.

Tukey promoted the use of the five number summary of numerical data:. His reasoning was that the median and quartiles, being functions of the empirical distribution, are defined for all distributions, unlike the mean and standard deviation.

Moreover, the quartiles and median are more robust to skewed or heavy-tailed distributions than traditional summaries the mean and standard deviation. Such problems included the fabrication of semiconductors and the understanding of communications networks. These statistical developments, all championed by Tukey, were designed to complement the analytic theory of testing statistical hypotheses.

Tukey held that too much emphasis in statistics was placed on statistical hypothesis testing confirmatory data analysis and more emphasis needed to be placed on using data to suggest hypotheses to test.

In particular, he held that confusing the two types of analyses and employing them on the same set of data can lead to systematic bias owing to the issues inherent in testing hypotheses suggested by the data.

Although EDA is characterized more by the attitude taken than by particular techniques, there are a number of tools that are useful. Many EDA techniques have been adopted into data mining and are being taught to young students as a way to introduce them to statistical thinking. Leave a Reply Cancel reply Your email address will not be published.

Terje Soerdal Very simply and nicely explained. Sayyid excellent explanation of the concepts 5th November at pm Reply to Sayyid.

Mustapha How do you then determine the sample size with the most minimal acceptable standard error. Osama Elbahr Thanks for your illustrations. But, can you clarify when to incorporate SE in our research results and how to interpret? Thanks again 19th February at pm Reply to Osama. Guru I was not able to understand standard error. Rohit Standard Deviation is the square root of variance, so its kind of trivial to state the conclusion about the increasing standard error with respect to standard error.

It is a good write up 6th October at pm Reply to Rohit. Emma Carter Thank you for flagging the symbol errors on the page Rohit. Wesley Hi, Thank you! Emma Carter Hi Wesley. Finance and banking is all about measuring and managing risk and standard deviation measures risk Volatility. Standard deviation is used by all portfolio managers to measure and track risk. One of the most important ratios in portfolio management, Sharpe Ratio for which William Sharpe got a Nobel Prize uses Standard Deviation to measure risk adjusted return and hence provides incentives to portfolio managers to generate return by taking minimum risk.

There are scores of questions based on the concept of measuring standard deviation and related metrics. If you use Excel to find standard deviation, it not only provides you with StdevP function, but also with a plethora of other functions like: Stdev , StdevA , etc. You should try and understand these functions as well.

In one of the next tutorials, we will delve deeper into these functions. For any queries regarding the concepts or modeling in Excel, feel free to put your comments in the comments section below. Our Placements. Students Testimonials. Our Centers. Just drop in your details and our corporate support team will reach out to you as soon as possible.

The standard deviation is calculated as the square root of variance by determining each data point's deviation relative to the mean. If the data points are further from the mean, there is a higher deviation within the data set; thus, the more spread out the data, the higher the standard deviation.

Standard deviation is a statistical measurement in finance that, when applied to the annual rate of return of an investment, sheds light on that investment's historical volatility. The greater the standard deviation of securities, the greater the variance between each price and the mean, which shows a larger price range. For example, a volatile stock has a high standard deviation, while the deviation of a stable blue-chip stock is usually rather low.

Standard deviation is calculated as follows:. Standard deviation is an especially useful tool in investing and trading strategies as it helps measure market and security volatility —and predict performance trends. As it relates to investing, for example, an index fund is likely to have a low standard deviation versus its benchmark index, as the fund's goal is to replicate the index.

On the other hand, one can expect aggressive growth funds to have a high standard deviation from relative stock indices, as their portfolio managers make aggressive bets to generate higher-than-average returns. A lower standard deviation isn't necessarily preferable. It all depends on the investments and the investor's willingness to assume risk.

When dealing with the amount of deviation in their portfolios, investors should consider their tolerance for volatility and their overall investment objectives. More aggressive investors may be comfortable with an investment strategy that opts for vehicles with higher-than-average volatility, while more conservative investors may not. Standard deviation is one of the key fundamental risk measures that analysts, portfolio managers, advisors use. Investment firms report the standard deviation of their mutual funds and other products.

A large dispersion shows how much the return on the fund is deviating from the expected normal returns. Because it is easy to understand, this statistic is regularly reported to the end clients and investors. Variance is derived by taking the mean of the data points, subtracting the mean from each data point individually, squaring each of these results, and then taking another mean of these squares. Standard deviation is the square root of the variance. The variance helps determine the data's spread size when compared to the mean value.

As the variance gets bigger, more variation in data values occurs, and there may be a larger gap between one data value and another. If the data values are all close together, the variance will be smaller.

However, this is more difficult to grasp than the standard deviation because variances represent a squared result that may not be meaningfully expressed on the same graph as the original dataset.