![]() ![]() The standard deviation for a population is represented by σ, and the standard deviation for a sample is represented by s. The standard deviation is the square root of the variance. N represents the number of units in the sample The Variance of a sample s 2 (pronounced s squared ) is expressed by a slightly different formula: N represents the number of units in the population X i represents the ith unit, starting from the first observation to the last The population Variance σ 2 (pronounced sigma squared ) of a discrete set of numbers is expressed by the following formula: In a normal distribution, about 68% of the values are within one standard deviation either side of the mean and about 95% of the scores are within two standard deviations of the mean. The standard deviation of a normal distribution enables us to calculate confidence intervals. Outlier Calculator An outlier is defined as any observation in a dataset that is 1.5 IQRs greater than the third quartile or 1.5 IQRs less than the first quartile, where IQR stands for interquartile range and is the difference between the first and third quartile. Therefore, if all values of a dataset are the same, the standard deviation and variance are zero. The smaller the variance and standard deviation, the more the mean value is indicative of the whole dataset. Where a dataset is more dispersed, values are spread further away from the mean, leading to a larger variance and standard deviation. ![]() In datasets with a small spread all values are very close to the mean, resulting in a small variance and standard deviation. They summarise how close each observed data value is to the mean value. The variance and the standard deviation are measures of the spread of the data around the mean. Measures of spread summarise the data in a way that shows how scattered the values are and how much they differ from the mean value. As discussed in the Measures of Central Tendency page, the mode, median, and mean summarise the data into a single value that is typical or representative of all the values in the dataset, but this is only part of the 'picture' that summarises a dataset. Summarising the dataset can help us understand the data, especially when the dataset is large. The spread of the values can be measured for quantitative data, as the variables are numeric and can be arranged into a logical order with a low end value and a high end value. Measures of spread include the range, quartiles and the interquartile range, variance and standard deviation. For interquartile range calculation, please enter numerical data separated with comma (or space, tab, semicolon, or newline). See also interquartile range and quartiles.Measures of spread describe how similar or varied the set of observed values are for a particular variable (data item). Values higher than Q3+1.5xIQR or lower than Q1-1.5xIQR are considered outliers and are plotted above the top whisker or below the bottom whisker. The ends of the whiskers are marked by two shorter horizontal lines. The vertical lines protruding from the box extend to the minimum and the maximum values of the data set, as long as these values are not outliers. The horizontal line inside the box is the median. best measurement when a data set contains several outliers or extreme values. Therefore the vertical width of the central box represents the inter-quartile deviation. Finding the Mean and the Median Using the TI-83, 83+, 84, 84+ Calculator. The bottom side of the box represents the first quartile, and the top side, the third quartile. The box plot is also referred to as box and whisker plot or box and whisker diagram Elements of the box plot What is a box plotĪ box plot is a diagram that gives a visual representation to the distribution of the data, highlighting where most values lie and those values that greatly differ from the norm, called outliers. These measures are displayed to the left of the chart.For more details on the dispersion of the data set, you may click on the More dispersion data link located on the left of the plot. When you submit your data, the server calculates the measures that will be used to plot the diagram. To clear the graph and enter a new data set, press "Reset". Press the "Submit Data" button to create the plot.You may also copy and paste data from another window such as an open document, spreadsheet pdf file or another web page. You do not need to specify whether the data is from a population or a sample. Individual values may be entered on separate lines or separated by commas, tabs or spaces. You must enter at least 4 values to build the box plot. Here is a simple online outlier calculator which is used to find lower and upper class boundaries from the given set of numbers with ease. This page allows you to create a box plot from a set of statistical data:
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