# Individual Discrete And Continuous Series In Statistics Pdf

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Published: 10.05.2021  There are several kinds of mean in mathematics , especially in statistics :. For a data set , the arithmetic mean , also known as average or arithmetic average, is a central value of a finite set of numbers: specifically, the sum of the values divided by the number of values. The arithmetic mean of a set of numbers x 1 , x 2 ,

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## Discrete vs continuous data

We shall continue our discussion on frequency distributions in this article by moving on to Frequency Distributions of Discrete and Continuous Variables. Table No.

For a continuous variable if we take a class for each distinct value of the variable, the number of classes will become unduly large, thus defeating the purpose of tabulation. In fact, since a continuous variable can assume an infinite number of values within its range of variation, the classification or sub-division of such data is necessarily artificial. Some guidelines that should be followed while dividing continuous data into classes are as follows:. Let us consider the following example regarding daily maximum temperatures in in a city for 50 days.

Class Interval: The whole range of variable values is classified in some groups in the form of intervals. Each interval is called a class interval. Class Frequency: The number of observations in a class is termed as the frequency of the class or class frequency.

Relative Frequency: Relative frequency is defined as the proportion of observations corresponding to a particular value of the variable or a class of values of the variable. Relative frequency of a particular value of the variable or a class of values of the variable is obtained by dividing the frequency corresponding to that particular value or that particular class by the total number of observations in the data set, i.

Relative frequency of any value or any class lies between 0 and 1. We calculate relative frequency if we want an idea about the relative importance of the particular value or class in relation to the total frequency. Percent Frequency: Sometimes Relative frequency is expressed in percent as i. Expressed as percents, the percent frequency of all values or all the classes must add up to Class limits are the two endpoints of a class interval which are used for the construction of a frequency distribution.

The lowest value of the variable that can be included in a class interval is called the lower class limit of that class interval. The highest value of the variable that can be included in a class interval is called the upper class limit of that class interval.

These are not the real limits or endpoints of a class interval. Hence, class limits are called apparent limits of a class. Let us take for example, Table No. The class intervals are , , , and Here, say for the class , the lower class limit is 17 and the upper class limit is However, if there was an observation of An observation of Again if there was an observation of Hence, effectively, the two actual endpoints of the class are These are actual or true limits of the class.

The two real endpoints of a class interval are called class boundaries. These are also called the real class limits. The basic rule is that class limits should have the same decimal place as the data set, but class boundaries should have one decimal place more. For example, let us say that we have the following data set on weight of a group of students in Kg : Here the class limits should have one decimal place and the class boundaries two decimal places. We obtain class boundaries from class limits by dividing the difference between the upper limit of a class and the lower limit of the next higher class into two equal parts.

Say, we are considering the classes and Again we have. We add 0. So, the class boundaries are For the class It should be noted that the upper class boundary of the lower class coincides with the upper class boundary of the next higher class.

This will give rise to confusion. Where should we include an observation which reads The answer is This is because the rule is that the frequency corresponding to a class denotes the number of observations Lower Class Boundary but Upper Class Boundary.

This is called the method of left inclusion. By including the lower class boundary but not the upper class boundary in the class we eliminate confusion about where to place an observation that happens to fall on a class boundary point. Open-end classes: It may be so that some values in the data set are extremely small compared to the other values of the data set and similarly some values are extremely large in comparison.

Then what we do is we do not use the lower limit of the first class and the upper limit of the last class. Such classes are called open end classes. Class width: The length of the class is called the class width.

It is also known as class size. Class mark: The midpoint of a class interval is called class mark. It is the representative value of the entire class. Frequency Density: It is the frequency per unit width of the class.

It is given by:. Frequency densities are essential to compare two classes of unequal width. For classes equal class widths frequency densities are proportional to the class frequencies. Relative Frequency Density: Relative frequency density of a class is relative frequency divided by the class width. The following data are based on the responses of 50 employees of a certain office on the distances in Km between their residence and workplace:.

Your email address will not be published. Number of car accidents Frequency 3 5 4 9 5 11 6 4 7 1 Total 30 Frequency Distribution of a Continuous Variable For a continuous variable if we take a class for each distinct value of the variable, the number of classes will become unduly large, thus defeating the purpose of tabulation. Some guidelines that should be followed while dividing continuous data into classes are as follows: The classes should be mutually exclusive, i.

No two classes should contain the same interval of values of the variable. The classes should be exhaustive, i. The number of classes and the width of each class should neither be too small nor too large. In other words, there should be relatively fewer classes if the difference between the least value of the variable and its highest value is small and relatively more classes if the same difference is large.

This difference between the least value of the variable and the greatest value of the variable is called the range of the variable or the data set. The classes should, preferably, be of equal width. Class Intervals Temperatures in Frequency 17 7 10 9 7 Total 50 Defining few terms Class Interval: The whole range of variable values is classified in some groups in the form of intervals. Class limits and Class boundaries: Class limits are the two endpoints of a class interval which are used for the construction of a frequency distribution.

It is given by: Frequency densities are essential to compare two classes of unequal width. It is given by: Exercise 1. The following data are based on the responses of 50 employees of a certain office on the distances in Km between their residence and workplace: 1. Comments great lesson. I wanted a solution of finding frequencies of both discrete and continuous data. ## Discrete vs Continuous Data: with Comparison Chart

Around this value, there is high concentration of the values. It is neither the central value nor the total sum of series which makes any effect on it. Every distribution cannot have a unique value of Mode. It can have two or even more than two modal values. The terms are arranged in any order. Ascending or Descending. If each term of the series is occurring once, then there is no mode, otherwise the value that occurs Maximum Times is known as Mode.

The classification of data as a frequency distribution has an inherent shortcoming. While it summarises the raw data making it concise and comprehensible, it does not show the details that are found in raw data. There is a loss of information in classifying raw data though much is gained by summarising it as a classified data. Once the data are grouped into classes, an individual observation has no significance in further statistical calculations. For example : the class 20—30 contains 6 obervations : 25, 25, 20, 22, 25 and So when these data are grouped as a class 20—30 in the frequency distribution,the latter provides only the number of records in that class i. All values in this class are assumed to be equal to the middle value of teh class interval or class mark i.

Earn a free Open University digital badge if you complete this course, to display and share your achievement. Anyone can learn for free on OpenLearn, but signing-up will give you access to your personal learning profile and record of achievements that you earn while you study. Start this free course now. Just create an account and sign in. Enrol and complete the course for a free statement of participation or digital badge if available. Discrete data is information that can only take certain values. Statistical Series. Individual Series. Frequency Series. Raw data. Individual series. Discrete Series. Continuous series. Inclusive series. Exclusive series.

## Frequency Distribution of Discrete and Continuous Variables

In statistics, data is defined as the facts and figures collected together for the purpose of analysis. It is divided into two broad categories, qualitative data, and quantitative data. Further, the qualitative data is cannot be measured in terms of numbers and it is sub-divided into nominal and ordinal data. On the other hand, quantitative data is one that contains numerical values and uses range. It is sub-classified as discrete and continuous data. ### Everyday maths 2

We shall continue our discussion on frequency distributions in this article by moving on to Frequency Distributions of Discrete and Continuous Variables. Table No. For a continuous variable if we take a class for each distinct value of the variable, the number of classes will become unduly large, thus defeating the purpose of tabulation. In fact, since a continuous variable can assume an infinite number of values within its range of variation, the classification or sub-division of such data is necessarily artificial. Some guidelines that should be followed while dividing continuous data into classes are as follows:. Let us consider the following example regarding daily maximum temperatures in in a city for 50 days.

The similarity is that both of them are the two types of quantitative data also called numerical data. However, in practice, many data mining and statistical decisions depend on whether the basic data is discrete or continuous. If you have quantitative data, like a number of workers in a company, could you divide every one of the workers into 2 parts? The answer is absolutely NOT. Sign in. Data Types are an important concept of statistics, which needs to be understood, to correctly apply statistical measurements to your data and therefore to correctly conclude certain assumptions about it. This blog post will introduce you to the different data types you need to know, to do proper exploratory data analysis EDA , which is one of the most underestimated parts of a machine learning project. Table of Contents:. Having a good understanding of t h e different data types, also called measurement scales, is a crucial prerequisite for doing Exploratory Data Analysis EDA , since you can use certain statistical measurements only for specific data types.

STATISTICS FOR ECONOMICS. How Arithmetic in case of continuous series is same as that of a discrete individual and discrete series. The value of Q1. Хорошо, а что, если… кошка. - Жила! - не задумываясь выпалил Беккер. - Жила. - Да.

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