Arithmetic mean is the amount secured by dividing the sum of the value of items in a series by their numbers. Here are the notes of chapter mean.
Topics Discussed
Types of Series
There are mainly three types of series as follows:
- Individual Series
- Discrete Series
- Continuous Series
Mean Formulas
Individual Series
- Direct Method: Mean = sum of x/N
- Shortcut Method: Mean = A + sigma(d)/N
A = Assumed Mean
d = X-A
N = Total Number of Terms
Discrete Series
- Direct Method: Mean = sigma(fx)/sigma(f)
- Shortcut Method: Mean = A + sigma(fd)/sigma(f)
- Step Deviation Method: Mean = A + sigma(fd’)/sigma(f)*c
Continuous Series
- Direct method: Mean = sigma(fm)/sigma(f)
- Shortcut Method: Mean = A + sigma(fd)/sigma(f)
- Step Deviation Method: Mean = A + sigma(fd’)/sigma(f)*c
d = m-A
d’ = d/c
Corrected Mean
Mean = sigma(X)[wrong] + Correct Value – Incorrect Value/N
Missing value
Mean = X1+X2+x3+…+Xn/N
Weighted Mean
Mean = sigma(XW)/sigma(W)
Note: If weights are not given in the question, weights can be given either in ascending or descending order.
Combined Arithmetic Mean
Combined Mean = M1N1+M2N2+…+MnNn/N1+N2+N3+…+N4
M1 = Mean 1
Concept of Economics and Significance of Statistics Notes
Merits of Arithmetic Mean
1) Simplicity
From the viewpoint of calculation and usage, the arithmetic mean is the simplest of all the measures of central tendency.
2) Certainty
The arithmetic mean is a certain value; it has no scope for estimated values.
3) Based on all items
The arithmetic mean is based on all the items in a series. It is, therefore, a representative value of the different items.
4) Algebraic Treatment
The arithmetic mean is capable of further algebraic treatment. It is, therefore, extensively used in statistical analysis.
Demerits of Arithmetic Mean
1) Effect of Extreme Value
The main defect of the arithmetic mean is that it gets distorted by extreme values of the series. Therefore, it is always an accurate measure.
2) Mean Value may not figure in the series at all
The mean value may sometimes be that value which does not figure in the series at all.
3) Unsuitability
The arithmetic mean is not a suitable measure in case of percentage or proportionate values.
So, these are the notes of arithmetic mean class 11 statistics. If you have any doubts related to this topic, you can comment below, I will try to resolve that.