Arithmetic Mean or Average is the most important factor in statistical calculations. It is easy understandable, easy to calculate and widely used not only in statistics. Using Arithmetic Mean, You should consider problems arising in the calculating process: it is taking averages of averages, it is distorted by outliers.
The Mode:
Is the value that occurs the most often:
3,4,5,8,4,6,4,6,5,99,……….. Mode is 4
In our case, The Mode is 19.
The Median:
The value in the middle of the data set when the data are arrayed in order of smallest to largest. In the case of an even number of observations, there is no clearly defined middle observation. The median is then taken as the mean of the two central observations:
9,10,10,10,11,12,13,14,16
In our data, the value in the middle is 18.
Standard Deviation:
In simple words, Standard Deviation shows us how far is the Data from Arithmetic Mean.
What influence do the Outliers have on the results?
If we looked at the results with the outliers and without them, Arithmetic Mean and Standard Deviation are the most depending on the Outliers factors. Standard Deviation has changed from 26.7 to 3.51 and there is no better evidence of the influence what The Outliers do have on the results. Make sure you have considered Outliers implementing the statistical calculations, otherwise the result will be incorrect.
Assume the above data represents the ages of all the people in your present class. Discuss whether your statistical results are accurate and representative.
Assuming current data I can not see a possibility it could represent the ages of all the people in my present class. Even without the Outliers the data the numbers are:
Mean: 18.39
Mode: 19
Median: 18
In other words the age that occurs the most is 19 years, the age in the middle is 18 years. The numbers speak of themselves. In our class, there are no people younger than 23 years, so the above data could not represent the ages of the people in the class.
The normal distribution is the most important in statistics. It occurs frequently when describing natural occurrences and is of particular importance in sampling theory and statistical inference. The main features are:
it is continuous distribution
it is a perfectly symmetrical bell shaped curve
the ‘tails’ of the distribution continually approach but never touch the horizontal axis
the mean, mode and median pass through the curve and bisect precisely the area under the curve into two equal halves.…
