Frequency table

Introduction to frequency table math: Collection of observations is the first step in statistical investigations. The numerical observations collected by an observer cannot be put to any use immediately and directly. That is why it is called a raw data. The raw data when put in ascending or descending order of magnitude is called an array or arrayed data.

Frequency table definition

According to frequency table definition : A Frequency table or frequency distribution is a method to present raw data in the form from which one can easily understand the information contained in the raw data.

Frequency table are of two types:
(i) Discrete frequency table distribution
(ii) Continuous or grouped frequency table distribution
Discrete frequency table distribution: The process of preparing this type of distribution is very simple. The construction of a discrete frequency distribution from the given raw data is done by the use of the method of tally marks. In the first column of the frequency table we write all possible values of the variable from the lowest to the highest.

Continuous or grouped table distribution: The above method of condensing the data is convenient only where the values in the raw data are largely repeating and the difference between the largest and the smallest observations is not very large.

How to do a frequency table?
If the number of observations is large, then arranging data in ascending or descending or serial order is a tedious job and it does not tell us much except perhaps the minimum and maximum of data.
Let us understand how to make a frequency table

In the first column of the table, we write all marks from lowest to highest. We now look at the first value in the given raw data and put a bar in the second column opposite to it. Now we see the second value in the given raw data and put a bar opposite to it in the second column. This process is repeated till all observations in the given raw data are exhausted. The bars drawn in the second column are known as tally marks and to facilitate we record tally marks in bunches of five, the fifth tally mark is drawn diagonally across the first four. We finally count the number of tally marks corresponding to each observation and write in the third column.
This way of representation of data is known as frequency distribution. Marks are called variates and the number of students who have secured a particular number of marks is called frequency of variate. The number of times an observation occurs in the given data, is called the frequency of observation.

Statistics Skewness

Statistics Skewness 

Skewness Statistics, Skewness is an asymmetry in the distribution of a sample data. When a sample data is graphically displayed, some distributions of the data have more observations on one side of the graph than the other side, this is called skewness. There are right and left skewness.  Distributions in which most of the observations are on the left that is towards the lower values, the skewness is said to be skewed right; and if the distribution in which most of the observations are on the right that is towards the higher values, the skewness is said to be skewed left. So, skewness statistic or skewness is the measure of symmetry or otherwise the lack of symmetry. A distribution when displayed on a graph is said to be symmetric if it looks the same to the right and left of a vertical line drawn in the centre point, just like mirror images.

Skewness in Statistics: In statistics, many statistical analyses fundamental task is to characterize the location and variability of a set of data. Skewness is one of the further characterizations of a data set. Skewness is the measure of symmetry of a frequency distribution of a data set. A sample data with symmetric distribution when graphically displayed shows a ‘hump’ like curve in the middle of the distribution and a tail type of lines on either side. The skewness in such cases is said to be zero. When distributions with large number of frequency scores are seen at the lower end of the distribution which have a tail like line pointing towards higher values and a ‘hump’ like curve over the smaller values; the skewness is said to be positive or the distribution is skewed right. When the distribution with large number of frequency scores are seen at the higher end of the distribution which have a tail like line point towards lower values and a ‘hump’ like curve over the higher values; the skewness is said to be negative or the distribution is skewed left.

Definition of Skewness : Skewness can be defined as the degree to which a statistical distribution is asymmetrical around the mean. In a perfectly symmetric distribution, the skewness is zero.  Distributions that have extreme values or outliners above the mean are said to be positively skewed or skewed right. Distributions that have extreme values or outlines below the mean are said to be negatively skewed or skewed left. In a given data with single variable, we can calculate skewness which is the sum of the deviations from the mean, raised to the third power, divided by number of data items minus 1, times the standard deviation raised to the third power.