Why is measures of dispersion important

In the above example, Coefficient of range. Advantages of Range : Range is easy to understand and is simple to compute. Disadvantages of Range : It is very much affected by the extreme values. It does not depend on all the observations, but only on the extreme values. Range cannot be computed in case of open-end distribution. Uses of Range : It is popularly used in the field of quality control. In stock-market fluctuations range is used.

Mean Deviation or Average Deviation : Mean deviation and standard deviation, however, are computed by taking into account all the observations of the series, unlike range. Definition : Mean deviation of a series is the arithmetic average of the deviations of the various items from the median or mean of that series. Median is preferred since the sum of the deviations from the median is less than from the mean. So the values of mean deviation calculated from median is usually less than that calculated from mean.

Mode is not considered, as its value is indeterminate. Mean deviation is known as First Moment of dispersion. Importance of Dispersion: We know that the object of measuring dispersion is to ascertain the degree of deviation which exist in the data and hence, the limits within which the data will vary in some measurable variate or attribute or quality. This object of dispersion is of great importance and occupies a unique position in statistical methods. Measures of dispersion supplement the information given by the measures of central tendency:.

It affords an estimate of the phenomena to which the given original data relate. This will increase the accuracy of statistical analysis and interpretation and we can be in a position to draw more dependable inferences. These values are then summed to get a value of 0. We need to find the average squared deviation. Common-sense would suggest dividing by n , but it turns out that this actually gives an estimate of the population variance, which is too small. This is because we are using the estimated mean in the calculation and we should really be using the true population mean.

It can be shown that it is better to divide by the degrees of freedom, which is n minus the number of estimated parameters, in this case n An intuitive way of looking at this is to suppose one had n telephone poles each meters apart. How much wire would one need to link them? As with variation, here we are not interested in where the telegraph poles are, but simply how far apart they are. A moment's thought should convince one that n -1 lengths of wire are required to link n telegraph poles.

From the results calculated thus far, we can determine the variance and standard deviation, as follows:. It is this characteristic of the standard deviation which makes it so useful. It holds for a large number of measurements commonly made in medicine. In particular, it holds for data that follow a Normal distribution.

Standard deviations should not be used for highly skewed data, such as counts or bounded data, since they do not illustrate a meaningful measure of variation, and instead an IQR or range should be used. In particular, if the standard deviation is of a similar size to the mean, then the SD is not an informative summary measure, save to indicate that the data are skewed. Skip to main content. Create new account Request new password. You are here 1b - Statistical Methods.

Measures of Location and Dispersion and their appropriate uses Statistics: Measures of location and dispersion This section covers Mean Median Mode Range Interquartile Range Standard deviation Measures of Location Measures of location describe the central tendency of the data.

Median The median is defined as the middle point of the ordered data. Example 1 Calculation of mean and median Consider the following 5 birth weights, in kilograms, recorded to 1 decimal place: 1. Advantages and disadvantages of the mean and median The major advantage of the mean is that it uses all the data values, and is, in a statistical sense, efficient.

Mode A third measure of location is the mode. Measures of Dispersion or Variability Measures of dispersion describe the spread of the data. Range and Interquartile Range The range is given as the smallest and largest observations. Click on the "Atmosphere" link. Click on the "monthly" link. Click on the "cloud cover" link under the Datasets and Variables subheading.

Press the Restrict Ranges button and then the Stop Selecting button. Higher lower values represent a larger smaller distribution of monthly cloud cover about the mean.

After completing the example, try going back and selecting the RMS over "T" command to see the difference between the two functions. View Root Mean Square Values To see the results of this operation, choose the viewer window with coasts outlined. High RMSA values correspond to areas with large interannual cloud cover variability.

Interquartile Range IQR Calculated by taking the difference between the upper and lower quartiles the 25th percentile subtracted from the 75th percentile. A good indicator of the spread in the center region of the data.

Relatively easy to compute. More resistant to extreme values than the range. Doesn't incorporate all of the data in the sample, compared to the median absolute deviation discussed later in the section. Also called the fourth-spread. Example : Find the interquartile range of climatological monthly precipitation in South America for January to December Select the "multi-satellite" link under the Datasets and Variables subheading.

Select the "precipitation" link again under the Datasets and Variables subheading. Choose the Monthly Climatology command. Enter the following lines under the text already there: [T]0. CHECK The replacebypercentile calculates the upper and lower quartiles for each grid point in the spatial field over the January to December climatologies.

The differences command then takes the difference of the two values along the percentile grid. The result is a dataset of interquartile ranges at each grid point in the spatial field. View Interquartile Range To see the results of this operation, choose the viewer window with coasts outlined.

The Amazon Basin exhibits high intraannual precipitation variability, while areas to the north and south exhibit lower precipitation variability. Example : Find the median absolute deviation of climatological monthly precipitation in South America for January to December We give below some definitions of dispersion as given by different statisticians from time to time:. Dispersion, in general sense, also indicates the lack of uniformity in the size of items of a series. Dispersion is said to be significant when variation or lack of uniformity in the size of items of a series is great aid substantial.

If the variability is less, dispersion is insignificant. This averaged deviation or dispersion is nothing else, but the average of the second order. Thus these second order averages represent the series and help in comparisons with other similar series. We know that the object of measuring dispersion is to ascertain the degree of deviation which exist in the data and hence, the limits within which the data will vary in some measurable variate or attribute or quality.

This object of dispersion is of great importance and occupies a unique position in statistical methods. Measures of dispersion supplement the information given by the measures of central tendency:. It affords an estimate of the phenomena to which the given original data relate. This will increase the accuracy of statistical analysis and interpretation and we can be in a position to draw more dependable inferences.

If the original data is expressed in different units, comparisons will not be possible. But with the help of relative measures of dispersion, all such comparisons can be easily made. Accurate and dependable comparison between the variability of two series will lead to dependable and accurate results.