The larger variance and standard deviation in Dataset B further demonstrates that Dataset B is more dispersed than Dataset A. Also, it is a calculation of variation while dividing a data set into quartiles. It is a measure of statistical distribution, which is equal to the difference between the upper and lower quartiles. The population variance \(\sigma^2\) (pronounced sigma squared) of a discrete set of numbers is expressed by the following formula: The interquartile range (IQR) is the difference between the upper and lower quartile of a given data set and is also called a midspread. 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. Therefore, if all values of a dataset are the same, the standard deviation and variance are zero. When a distribution is skewed, and the median is used instead of the mean to show a central tendency, the appropriate measure of variability is the Interquartile range. Outliers are individual values that fall outside of the overall pattern of a data set. The interquartile range (IQR) is the range of values that resides in the middle of the scores. The interquartile range rule is useful in detecting the presence of outliers. The smaller the variance and standard deviation, the more the mean value is indicative of the whole dataset. The interquartile range (IQR) is the difference of the first and third quartiles. 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.
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