Name 3 measures of dispersio
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The mean is calculated by adding together all the values (54+54+54+55+56+57+57+58+58+60+60 = 623) and dividing by the number of observations (11) which equals 56.6 years. This is also known as the arithmetic average. The mean is the sum of the value of each observation in a dataset divided by the number of observations. The median cannot be identified for categorical nominal data, as it cannot be logically ordered. The median is less affected by outliers and skewed data than the mean, and is usually the preferred measure of central tendency when the distribution is not symmetrical. In the following distribution, the two middle values are 56 and 57, therefore the median equals 56.5 years:ĥ2, 54, 54, 54, 55, 56, 57, 57, 58, 58, 60, 60 When the distribution has an even number of observations, the median value is the mean of the two middle values. Looking at the retirement age distribution (which has 11 observations), the median is the middle value, which is 57 years: In a distribution with an odd number of observations, the median value is the middle value.
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The median divides the distribution in half (there are 50% of observations on either side of the median value). The median is the middle value in distribution when the values are arranged in ascending or descending order. In cases such as these, it may be better to consider using the median or mean, or group the data in to appropriate intervals, and find the modal class. In some cases, particularly where the data are continuous, the distribution may have no mode at all (i.e. The presence of more than one mode can limit the ability of the mode in describing the centre or typical value of the distribution because a single value to describe the centre cannot be identified. It is also possible for there to be more than one mode for the same distribution of data, (bi-modal, or multi-modal). When the distribution of retirement age is ordered from lowest to highest value, it is easy to see that the centre of the distribution is 57 years, but the mode is lower, at 54 years.ĥ4, 54, 54, 55, 56, 57, 57, 58, 58, 60, 60 In some distributions, the mode may not reflect the centre of the distribution very well. The are some limitations to using the mode. The mode has an advantage over the median and the mean as it can be found for both numerical and categorical (non-numerical) data. The most commonly occurring value is 54, therefore the mode of this distribution is 54 years.