BUSINESS STATISTICS NOTESB.COM 2ND AND 3RD SEM NEW SYLLABUS (CBCS PATTERN) MEASURE OF CENTRAL TENEDENCY (AVERAGE)
Meaning of Average
One of the most important purposes of statistical analysis is to find a single value that describes the features of a large amount of data. Such a value is called the average value or “average” or the expected value of a variable.
In the words of Croxton and Cowden, “A median value is one value within the range of data used to represent all values in a series.”
According to Clark, "Measurement is an attempt to obtain a single calculation to define all values."
From the above definition we can say that the ratio is a single value representing a set of values. Displays feature for the whole group. The average value is between the maximum and minimum values of a series. That is why it is also called the average inclination rate.
Measurement objectives
The purpose of the average survey is listed below:
a) Finding a single number that describes a feature of the whole group.
b) Facilitate comparisons of data over a period of time or at a particular time.
Requirements for good rating
The following are some important factors that should satisfy a good standard
1. It should be easy to understand.
2. It should be easy to calculate.
3. It should be based on all things.
4. Excessive prices should not be affected.
5. It should be strongly defined.
6. Must be able to continue treatment for algebra.
Types of scale
The rating is divided into three main categories:
a) The definition is also divided into: Arithmetic mean, Weighted Mean, Geometric Mean and Harmonic Mean.
b) Median and
c) Mode
Arithmetic Mean: Definition, Structures, Qualifications and Qualifications
It is the value obtained by combining all the elements and dividing the value by the number of objects. Also called a measure. It is the most popular and widely used measure to represent all data at a single value.
The definition of Arithmetic may be:
(i) A simple arithmetic definition, or
(ii) Definitive arithmetic definition.
Arithmetic features mean:
1. The total deviation from the arithmetic definition is zero ∑ (X – X) = 0.
2. Total square deviation of items from A.M. minimum, less than the sum of the square deviation of items from any other values.
3. If each item in the series is replaced by a description, the amount of this change will be equal to the amount of each item.
Benefits of A.M .:
(i) It is easy to understand and easy to calculate.
(ii) It affects the value of everything in the series.
(iii) It is strongly defined.
(iv) Able to continue treatment for algebra.
(v) The value is calculated and is not based on location in the series.
Benefits of A.M .:
(i) It is affected by the extremes i.e., the smallest and largest objects.
(ii) It is not possible to detect by examination.
(iii) In some cases A.M. does not represent the real thing. For example, the average number of patients admitted to a hospital is 10.7 per day.
(iv) A.M. not suitable for extremely equitable distribution.
Definition of Geometry (GM): Definition, Use, Applicability and Evil
It is defined as the nth root of the product of n objects or values. that is, G.M. = n√ (x1. x2. x3 …… xn)
Benefits of G.M .:
(i) Excesses in the series are not affected.
(ii) It is strongly defined and its value is a straightforward figure.
(iii) Able to continue the treatment of algebra.
(iv) It is useful for calculating reference number.
Benefits of G.M .:
(i) It is difficult to understand and calculate.
(ii) It cannot be calculated if one of the values is 0 or negative.
Use of G.M .:
(i) It is used to determine the rate of change.
(ii) It is useful in estimating population growth.
(iii) It is considered to be the best measure for the construction of reference numbers.
Harmonic Mean (HM): Definition, Use, Benefits and Qualifications
It is defined as the repetition of the arithmetic meaning of the repetition of each observation.
N
H.M.
=
(1 / x1 + 1 / x2 + 1 / x3 + ........ + 1 / xn)
Benefits of H.M .:
(i) Like AM and GM, it is also based on all observations.
(ii) The most appropriate measure under the conditions of wide variation between series objects as it provides maximum weight to small objects.
(iii) Able to continue the treatment of algebra.
(iv) It is very useful when measuring certain types of scales and scales.
Benefits of H.M .:
(i) It is difficult to understand and calculate.
(ii) It cannot be calculated if one of the values is 0 or negative.
(iii) You need to know all the items in the series before they can be counted.
(iv) It is usually an amount that may not be a member of a given set of numbers.
Use of H.M .: If two measurements are taken together to measure variables, HM may be used. For example, tons of mileage, speed per hour. In the example above of the tone meter, a ton is one measure and a mile is another measure. HM is used to calculate average speed.
Median: Definition, Benefits and Qualifications
Median can be defined as the size (real or limited) of an object in the middle of an ascending or descending series of its magnitude. It is in the middle of the series and divides the series into two equal parts. Median is also known as the average position.
Median Benefits:
(i) It is easy to understand and easy to forget, especially single and separate series.
(ii) Excesses in the series are not affected.
(iii) It can be determined by drawings.
(iv) In open classes, median can be counted.
(v) It can be obtained by testing, after sorting the data in order of magnitude.
Median Benefits:
(i) It does not consider all variables because it is a local measure.
(ii) Median value