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. Typical graphical techniques used in EDA are:. These EDA techniques aim to position these plots so as to maximize our natural pattern-recognition abilities. A clear picture is worth a thousand words! Privacy Policy. Skip to main content. Measures of Variation. Search for:. Describing Variability.
Range The range is a measure of the total spread of values in a quantitative dataset. Learning Objectives Interpret the range as the overall dispersion of values in a dataset. Key Takeaways Key Points Unlike other more popular measures of dispersion, the range actually measures total dispersion between the smallest and largest values rather than relative dispersion around a measure of central tendency.
Because the information the range provides is rather limited, it is seldom used in statistical analyses. The mid-range of a set of statistical data values is the arithmetic mean of the maximum and minimum values in a data set.
Key Terms range : the length of the smallest interval which contains all the data in a sample; the difference between the largest and smallest observations in the sample dispersion : the degree of scatter of data. Variance Variance is the sum of the probabilities that various outcomes will occur multiplied by the squared deviations from the average of the random variable. Learning Objectives Calculate variance to describe a population.
Key Terms deviation : For interval variables and ratio variables, a measure of difference between the observed value and the mean. Standard Deviation: Definition and Calculation Standard deviation is a measure of the average distance between the values of the data in the set and the mean.
Learning Objectives Contrast the usefulness of variance and standard deviation. Key Takeaways Key Points A low standard deviation indicates that the data points tend to be very close to the mean; a high standard deviation indicates that the data points are spread out over a large range of values. In addition to expressing the variability of a population, standard deviation is commonly used to measure confidence in statistical conclusions. To calculate the population standard deviation, first compute the difference of each data point from the mean, and square the result of each.
Next, compute the average of these values, and take the square root. Key Terms normal distribution : A family of continuous probability distributions such that the probability density function is the normal or Gaussian function.
Interpreting the Standard Deviation The practical value of understanding the standard deviation of a set of values is in appreciating how much variation there is from the mean. Learning Objectives Derive standard deviation to measure the uncertainty in daily life examples. Key Takeaways Key Points A large standard deviation indicates that the data points are far from the mean, and a small standard deviation indicates that they are clustered closely around the mean.
In finance, standard deviation is often used as a measure of the risk associated with price-fluctuations of a given asset stocks, bonds, property, etc. Key Terms standard deviation : a measure of how spread out data values are around the mean, defined as the square root of the variance disparity : the state of being unequal; difference.
Using a Statistical Calculator For advanced calculating and graphing, it is often very helpful for students and statisticians to have access to statistical calculators. Key Terms TI : A calculator manufactured by Texas Instruments that is one of the most popular graphing calculators for statistical purposes. R : A free software programming language and a software environment for statistical computing and graphics. Degrees of Freedom The number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary.
Key Takeaways Key Points The degree of freedom can be defined as the minimum number of independent coordinates which can specify the position of the system completely. A parameter is a characteristic of the variable under examination as a whole; it is part of describing the overall distribution of values.
As more degrees of freedom are lost, fewer and fewer different situations are accounted for by a model since fewer and fewer pieces of information could, in principle, be different from what is actually observed. Key Terms residual : The difference between the observed value and the estimated function value. Interquartile Range The interquartile range IQR is a measure of statistical dispersion, or variability, based on dividing a data set into quartiles. Learning Objectives Calculate interquartile range based on a given data set.
Key Terms outlier : a value in a statistical sample which does not fit a pattern that describes most other data points; specifically, a value that lies 1.
Measures of Variability of Qualitative and Ranked Data Variability for qualitative data is measured in terms of how often observations differ from one another.
Learning Objectives Assess the use of IQV in measuring statistical dispersion in nominal distributions. Instead, we should focus on the unlikeability, or how often observations differ. An index of qualitative variation IQV is a measure of statistical dispersion in nominal distributions —or those dealing with qualitative data.
The variation ratio is the simplest measure of qualitative variation. It is defined as the proportion of cases which are not the mode. Key Terms variation ratio : the proportion of cases not in the mode qualitative data : data centered around descriptions or distinctions based on some quality or characteristic rather than on some quantity or measured value.
Distorting the Truth with Descriptive Statistics Descriptive statistics can be manipulated in many ways that can be misleading, including the changing of scale and statistical bias. Learning Objectives Assess the significance of descriptive statistics given its limitations. Key Takeaways Key Points 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.
Descriptive statistics, however, lacks the ability to identify the cause behind the phenomenon, correlate associate data, account for randomness, or provide statistical calculations that can lead to hypothesis or theories of populations studied. 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.
Key Terms bias : Uncountable Inclination towards something; predisposition, partiality, prejudice, preference, predilection. Thank you for the comment.
There is indeed a different formula, which uses n — 1 rather than N, when calculating the standard deviation of a sample. The resource here provides a really good explanation too.
Hope that proves useful. Conducting successful research requires choosing the appropriate study design. This article describes the most common types of designs conducted by researchers. What are the key steps in EBM? Who are S4BE? Eveliina Ilola View more posts from Eveliina. 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. Students Testimonials. Our Centers. Just drop in your details and our corporate support team will reach out to you as soon as possible.
Just drop in your details and our Course Counselor will reach out to you as soon as possible. Just drop in your details and start downloading material just created for you. Contact now for Free Counselling! What is Standard Deviation? Spread the love. Related links you will like:. Fee Enquiry. Get Free Counselling. Join Us. Actively scan device characteristics for identification. Use precise geolocation data. Select personalised content.
Create a personalised content profile. Measure ad performance. Select basic ads. Create a personalised ads profile. Select personalised ads. Apply market research to generate audience insights. Measure content performance. Develop and improve products. List of Partners vendors. Two of the most popular ways to measure variability or volatility in a set of data are standard deviation and average deviation, also known as mean absolute deviation.
Though the two measurements are similar, they are calculated differently and offer slightly different views of data. Determining volatility—that is, deviation from the center—is important in finance, so professionals in accounting, investing, and economics should be familiar with both concepts.
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