A very widely used method in statistics is the finding of average from a given set of data.
Often people are interested in finding the middle most elements from a given set of data.
There are namely three methods by which you can find the average from a given data set. You can make use of the mean, median and mode and calculate the results. Each method mentioned here will give you a different way to view the numbers.
The way in which the question has been framed, will actually determine which method would be most useful in solving that question.
Mean and median
Finding the mean is the most common way of getting the average from a given set of data. In the everyday jargon, the words mean and average are often used interchangeably. To find this mean, is rather simple and requires you to add up the data and then divide it by the number of data entries present.
The median on the other hand, requires you to find the middle value from a given number set. Different data however needs to be arranged in ascending or descending order before finding out him average.
Range and mode
Use of mode to find out the average is not quite common. Final results that you will get from it are also not quite very useful in nature. A certain number that would occur the most number of times in a particular set is its mode.
You can get more than one mode from a set of data or nothing at all. Range belonging to a set of data is strictly not its average, but is however taught together. This is because the range shows the extent to which a data set is spread. The difference existing between the smallest and largest value gives us a range.
Displaying data via histogram
By using histograms, data can be displayed in a very convenient manner. It looks quite familiar to a bar graph actually. Here, instead of individual data, a certain range of data is plotted. When your data set varies by a certain degree, then histograms are quite useful for plotting data. Histograms also have a certain bin width that can be varied. Data in a histogram is grouped by use of such bins. Individual values are not displayed in these histograms. However, it is quite a nice way of looking out for a certain trend of data.
Scatter plot for data
Scatter plots are a great way to display data having two variables. Different predictions can be made by making use of such data. Contrary to histograms, scatter plots, are able to represent individual values too. Neither histograms, nor box-whisker plots can represent individual data. Generally, it is seen, that the independent variable is represented on x-axis and the dependent one on y-axis. Trends which emerge finally from these plots give a very clear indication regarding what is required to be done.
Concept of correlation
By use of scatter plots, people often find out ways in which variables can get related to each other. This kind of relationship, in terms of statistics is known as correlation. Usually you will find that there are three types of correlations, namely positive, negative or none. In positive correlation, both variables are directly proportional to one another. In negative correlation, the two variables are inversely proportional to each other. If two variables are not related to each other in any manner, then it is termed as no correlation. One of these two variables either increases or decreases, it has no effect on the other.
Line of best fit
By making use of a line of best fit, different predictions can be made on data used in the past. There are lots of complex types of data that can be used in statistics in order to find this actual line. A certain line drawn through the graph needs to be fitting or going through the entire trend of data.
When you are drawing this particular line, you have to ensure that it fits into entire trend of the data. If there are points that are too much away, either higher or lower, than this line, then the line of best fit needs to be adjusted.
Applied statistics discussed
There are lots of real life problems that are required to be solved with usage of statistics. There are some basic techniques in statistics which includes t-tests, non-parametric analysis and correlations that can be used for solving these problems.
Emphasis is always given on application and not theory in different online courses. Certain software, like strata is used for performing the analyses. By taking help from online tutors, students will be able to distinguish between different statistical techniques and interpret results from analyses.
Getting grip on regression
Linear regression as well as multiple regressions is a part of statistics nowadays. A lot of statistical packages are used nowadays and attendants are required to understand and interpret output coming from linear regression from such packages.
There are many circumstances where linear regression is not really appropriate for use. Correct data type is always required to be used for doing your regression analysis. Visuals can be used to good effect for understanding concepts of linear regression. A certain degree of familiarity with descriptive statistics is required for solving stuffs related to regression.
The concepts associated with linear and certain generalized mixed model are becoming part of statistical courses more and more nowadays. These are essentially models associated with regression having fixed and random effects. As a result of this, they are also often termed as hierarchical linear models.
Students need to know about ways of running mixed models in commonly used software of statistics. There are longitudinal measures of data that get analyzed with use of these mixed models. Hypothesis testing is something that all students of statistics need to know well in order to complete these assignments quickly and correctly.
Use of Variance
Variance in statistics is actually the probability of squared deviation of any random variable derived from its mean. In terms of layman, it is actually measuring the degree of how much a certain set of numbers are deviating from their normal average values.
Usage of variance is very much central to statistics and finds applications in many fields including descriptive statistics, hypothesis testing etc. Statistical analysis of data is something new in markets and is being done on a regular basis. The value of variance is actually the squared value of standard deviation. It also has relationship with many other parts of statistics.
Measure of standard deviation
Standard deviation in statistics is used for measuring the amount of variation that a given set of data undergoes. When you encounter a standard deviation of low value, it means that the value is quite close to that of the mean. A higher value of standard deviation tells us that different data points are dispersed over a very wide range of values.
As mentioned earlier, it is the square root of variance from any given data set. A really useful property of this standard deviation is, that it can be expressed in units same as that of data that you would be working with.
Median absolute deviation
Median absolute deviation is also often referred to as MAD in statistics. It is a very useful measure of variation of a sample or data set. Population parameters calculated from any sample is also done by using MAD. While using MAD, deviations present in a smaller number of outliers are often deemed to be irrelevant.
Estimates can be made in a more robust manner by using MAD rather than variance or standard deviation. Cauchy distribution for example does not possess any mean or variance and can therefore be used with MAD effectively.
What are quintiles?
In topics concerned with statistics and probability, quantiles are essentially those points cutting up or dividing certain probability distributions. The distributions are mostly equally spaced. You must always remember that the number of quantiles present is always less than number of groups that you will get.
Therefore, a quartile will provide you with four equally sized groups and have three cut points. Certain quantiles have special names such as deciles which 10 groups. These groups themselves are given names such as halves, quarters etc.
Sampling distribution is termed as probability distribution of any random sample. You need to take into account a large number of samples having many observations in it. These observations were then used separately to compute one value of a statistic for each of these samples. Sampling distribution in that case would be probability distribution those values that the calculation would take in.
These sampling distributions are really important because they can provide a certain simplification while getting on to some kind of statistical inference. These distributions, allow you to make certain analytical considerations based on them. Joint probability distribution regarding each individual sample is therefore not required to be calculated.
Collection of data
Different methods used for collection in data in statistics need to be considered carefully for planning the whole research. This consequently has a huge effect on size of sample as well as further designing of the experiment. Data can be collected from people in form of questionnaires. The quantitative form of data gets collected by measuring the numbers got from various instruments. Some data can be simply obtained by use of metrics, whereas others are only obtained by observation. You can obtain data by whichever way you want. However, these data needs to be stored in an organized manner.
Why study statistics?
The first and foremost reason for engaging in study of statistics is to conduct research in an efficient manner. Different decisions based on a set of data would be very difficult to make, if you did not know, how to make use of statistics effectively.
Different possibilities are also thrown open when the interpretations of the data are complete. Different technical journals inevitably contain statistics in some form or the other. If you do not have any knowledge about statistics, you will not be able to understand any of the information presented in those papers or journals.
Knowing more about the data
Data being used in the statistical analysis is the most important part of statistics. All the data is always a part certain research and do not simply appear out of thin air. You need to ask certain questions for yourself before you go on working with the data. Suppose these questions originated from a survey, you should be knowing who conducted the poll and then interpreted the data.
The reason behind conducting such polls and what effect it would have on policy making is also needs to be known by you. When you know about these things, then no possible biases will creep into working with the data.
Develop of your analytical skills
Most of the students, who are even handling very rudimentary levels of statistics, have developed some sort of analytical skills while working with the data. A further study of different statistical methods will only further help in improving these skills.
Creative as well as logical levels of thinking are required in order to go forward in this field. Information needs be evaluated in a proper manner as conducting research is a rather time consuming as well as expensive process.
Application of statistics
Statistics is such a field, that data derived from it can be used in all kinds of disciplines. It finds application in geology, biology, analytics, the list is simply endless. Students will benefit greatly if they have knowledge about these different statistical methods.
Emma McCoy is a very popular professor and author who know the various domains concerned with statistics well. Emma is a professor of statistics, faculty of natural sciences and Department of Mathematics. Her research interests are Time Series, Computational statistics and Wavelets. She brings all these varied experiences on the table for students. She has done M.S. in Statistics from Hult International Business School. She has years of experience in the field and has earned the degree from the Harvard University which proves her potential to manage the queries of students. Through her unique teaching technique students gain clarity on the subject. For more information about her, you can find it here http://wwwf.imperial.ac.uk/~ejm/