Measures of Dispersion - Essay Example

A measure of central tendency is descriptive statistics and includes those values of data that tend to center. It includes meaning media and mode. Mean is the most familiar average. Many people use this measure as it is easy to calculate and gives very close to the accurate answer. However, still, this measure faces a lot of criticism for its weaknesses as it takes each and every number into account which makes it a lengthy task when data is huge. Mean also gets affected by extreme values. If the number is very large it will also tend towards the side which is greater than the mean and vice-versa. If the data has some extreme values, then the median becomes the most accurate measure of central tendency. However, one weakness of median is that it cannot be applied to raw data and the data has to be arranged in ascending or descending order. This indicates that this measure is time-consuming and when data is very large it is very difficult to first arrange it in ascending order and then arrive at the median. Mode is considered appropriate for nominal data and can be calculated very easily by observation. There are no calculations required when computing mode and hence it is very quick. The only disadvantage with the mode is that it gives the least accurate answer and hence people do not use it despite it being the easiest measure of center or central tendency.

But, as the numbers are squared in computing standard deviation, the extreme values get more weightage, and the answer is distorted. Similarly, variance is another good measure as it includes all the values in an observation. The only weakness of variance is that it is very time-consuming as each observation has to be squared.

The number of observations that fall into a particular class is called the frequency or count of that class. Frequency distribution is a table that lists all class and their frequencies in a systemized manner. This table tells us at a glance how many times a particular observation has been seen in our class.

For example, let’s suppose we are interested in finding out the speed of cars on a particular downtown road. We will first list down all the classes that we think are going to be observed. For example, in this case, our classes will be different speeds, such as 20-40 km/h, 40-60km/h. 60-80 km/h and so on. Now when we are going to observe these cars we are going to assign each car that is coming into downtown to one of these classes. Suppose the first car that we observed is being driven at twenty-five km/h. It is very clear that this car is going to be included in the class representing 20-40 km/h. Now we are going to assign cars to each class on the basis of their speed. After we have observed the required number of cars, we will be able to complete our frequency distribution table, which is going to look like this:

Intervals                             Frequency

20-40 Km/h                              5

41-60 Km/h                            12

6-810 Km/h                             13

Total                                       30

This table tells us that the total number of cars that were observed was 30. Out of these 30 cars 5 drove at a speed between 20-40 km/h, 12 drove at 41-60 km/h, whereas 13 cars drove at the speed of 61-80 km/h.