![]() ![]() The larger variance and standard deviation in Dataset B further demonstrates that Dataset B is more dispersed than Dataset A. The population variance \(\sigma^2\) (pronounced sigma squared) of a discrete set of numbers is expressed by the following formula: Range, variance, and standard deviation all measure the spread or variability of a data set in different ways. To find the mean, we add up all the results and then divide them by the number of swimmers: The median is the middle number in a list of numbers ordered from smallest to. The mean is the total of all the values, divided by the number of values. 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 mode is the value that appears most often in a set of data. The standard deviation of a normal distribution enables us to calculate confidence intervals. Definition: The mode of a set of data is the value in the set that occurs most often. Therefore, if all values of a dataset are the same, the standard deviation and variance are zero. This problem really asked us to find the mode of a set of 7 numbers. 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. ![]() Mean: The 'average' number found by adding all data points and dividing by the number of data points. They each try to summarize a dataset with a single number to represent a 'typical' data point from the dataset. The variance and the standard deviation are measures of the spread of the data around the mean. Mean, median, and mode are different measures of center in a numerical data set. ![]()
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