Descriptive Statistics Tutor

By Author: Pierce Brosnan
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Introduction to definition of descriptive statistics tutor:

Descriptive Statistics basically summarizes a large amount of quantitative way in a clear and understandable way. The clear and understandable way by which data can be represented could either be a Numerical Method or a Graphical Method.

Example of Descriptive Statistics: Given below are few of the examples of Descriptive statistics. Basically we can categorize the first 2 examples as a Numerical method of Descriptive statistics, While the last 3 examples as a graphical method of Descriptive statistics.

Measure of Central Tendency of a Data Set
Measure of Statistical Dispersion of a Data Set
Histogram
Boxplot
Scatterplot.

Use of Descriptive Statistics in Analysis: Descriptive Statistics helps us in reaching the conclusion in quicker and easier manner as it provides simple and easily understandable summaries about a data sample. Take for example, the shooting percentage of a NBA player would easily help us in analysing his performance. Another example would be the scores of a 12th grade student in terms of the ...
... GPA(Grade Point Average) or CGPA(Cumulative Grade Point Average) as the GPA or CGPA helps us in clearly identifying the performance of the student in his grade.

Descriptive Statistics using Numerical Methods

Numerical Methods used in the study of Descriptive Statistics basically help us in identifying the following two types of statistical measurements

1. Central Tendency: The mode, The Median and The Mean are the 3 main numerical measurements of the Central Tendency each of which can me mathematically expressed as below.

Mode: Mode is defined as the value which occurs the maximum number of times in a given data sample or the value which is having the greatest frequency.

Mean: Mean is the just the average of the given data sample. It is nothing but the sum of all the values in the data sample divided by the number of values in the data sample.

Median: Median is the measurement which seperates the data sample in to two equal halves. Above the Median lies the upper half of the data sample while the lower half of the data sample lies below the median.

2. Statistical Dispersion: The Range, Standard deviation and the Variance are the 3 main numerical measurements of the Statistical dispersion and can be expressed mathematically as below.

Range: Range in simple words is the measurement of data sample from the smallest sample to the largest sample and is sometimes called the spread of the data.

Variance: Variance is defined as the average of squared difference from the Mean of the Data Sample. In short it is difference between the actual value and the current value. Variance can be both positive and negative.

Standard Deviation: Standard Deviation is nothing but the square of the Variance or technically it can be defines as the average degree to which a value can deviate from its Mean.

Descriptive Statistics using Graphical Methods:

Graphical Methods used in the study of Descriptive statistics helps in representing the data sample in a visually pleasing and easily graspable manner. The three important methods that can be used to represent the data in a graphical way are as follows.

1. Histogram: Histogram is a visual representation of the data sample and was first introduces by Karl Pearson. It is an representation of the probability distribution of a continuous variable. A histogram is a continuous erection of vertical rectangles over a given interval of data with the height of the rectangle representing the frequency of data.

2. Box Plot: Box plot also known as a box-and-whisker diagram is a graphical representation of a given data sample in a 5 different number summaries namely the lowest or smallest observations, Lower quartile, Median Quartile, upper quartile and the largest or biggest observation.

3. Scatter Plot: A scatter plot or Scatter graph is a graphical representation of a given data sample in a graph using Cartesian coordinates. Basic limitation with scatter plot is that the data sample is always represented for a collection of points containing two variables, one plotted on the horizontal x-axis and the other on the vertical y-axis.

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