Students can go through AP Inter 2nd Year Economics Notes 10th Lesson Economic Statistics will help students in revising the entire concepts quickly.

## AP Inter 2nd Year Economics Notes 10th Lesson Economic Statistics

→ Dispersion is the measure of the variation of the items.

→ Measures of variation are needed for four basic purposes.

a. To determine the reliability of an average.

b. To serve as a basis for the control of variability.

c. To compare two or more series.

d. To facilitate the use of other statistical measures.

→ A good measure of dispersion should possess the following properties.

a. It should be simple, easy to understand.

b. It should be rigidly defined.

c. It should have sampling stability.

d. It should not affected by extreme items.

→ There are five methods of studying variation.

a. The range.

b. The interquartile range and the quartile deviation.

c. Mean deviation.

d. Standard deviation.

e. The Lorenz curve.

→ Range is the simplest method of studying dispersion. It is defined as the difference

between the value of the smallest item and the value of the largest item included in the distribution.

Range = L – S

→ Quartile deviation is the entire data is divided into four equal parts. Each containing 25% of the values, we get the values of quartiles and median.

Q.D = \(\frac{\mathrm{Q}_3-\mathrm{Q}_1}{2}\)

→ Mean deviation is two measures which are based upon deviation of the values from their average are mean deviation.

M.D = \(\frac{\Sigma \mathrm{f}|\mathrm{D}|}{\mathrm{N}}\)

→ Standard deviation, the deviation and first squared and average and then square root of the average is found.

σ = \(\sqrt{\frac{\Sigma \mathrm{d}^2}{\mathrm{~N}}}\)

→ Lorenz curve is a graphical measure. It is used for estimating dispersion.

→ Correlation is an analysis of the covariation between two or more variables.

→ There are different types of correlation. Commonly classified into positive or negative correlation. If the two variables move in the same direction the correlation said to be positive. If two variables move in opposite direction it is negative correlation.

→ The important statistical tools used to measure correlation are scatter diagrams, Karl Pearson’s coefficient of correlation and Spearman’s rank correlation.

→ Index numbers are devices for measuring difference in magnitude of groups of related variabilities.

→ There are four types of index numbers.

a. Price Index Number

- Wholesale price index number
- Retail price index number

b. Quantity Index Number

c. Cost living Index Number

d. Special purpose Index Number

Formulae

→ Laspeyre’s formula

Price index number P_{01} = \(\frac{\Sigma P_1 Q_0}{\Sigma P_0 Q_0} \times 100\)

Quantity index number Q_{01} = \(\frac{\Sigma P_0 Q_1}{\Sigma P_0 Q_0} \times 100\)

→ Paasche’s formula

Price index number P_{01} = \(\frac{\Sigma P_1 Q_1}{\Sigma P_0 Q_1} \times 100\)

Quantity index number _{01} = \(\frac{\Sigma P_1 Q_1}{\Sigma P_1 Q_0} \times 100\)

→ Bowley’s formula

Price index number P_{01} = \(\frac{L+P}{2}\)

Quantity index number Q_{01} = \(\frac{L+P}{2}\)

→ Fisher’s formula

Price index number P_{01} = \(\sqrt{L \times P}=\sqrt{\frac{\Sigma P_1 Q_0}{\Sigma P_0 Q_0}} \frac{\Sigma P_1 Q_1}{\Sigma P_0 Q_0} \times 100\)

Quantity index number_{01} = \(\sqrt{L \times P}=\sqrt{\frac{\Sigma P_0 Q_1}{\Sigma P_0 Q_0} \times \frac{\Sigma P_1 Q_1}{\Sigma P_1 Q_0}} \times 100\)

Fisher’ s formula satisfy the both time reversal test and factor reversal test.

→ Correlation : Correlation is an analysis of the co-variation between two or more variables. There are two types of correlaton.

- Karl Pearson’s method of correlation.
- Spearman’s Rank correlation.

1. Karl Pearson’s method of correlation r = \(\frac{\Sigma x y}{\sqrt{\Sigma x^2} \Sigma y^2}\)

2. Spearman’s rank correlation r_{k} = \(\frac{1-6 \Sigma D^2}{N^3-N}\)

→Index number : Index numbers are devices for measuring difference in the magnitude of groups related variabilities. There are four types of index numbers.

- Price index number
- Quantity index number
- Cost living index number
- Special purpose index number

→ Fisher’s price index formula :

P_{01} = \(\sqrt{L \times P}\)

= \(\sqrt{\frac{\Sigma P_1 Q_0}{\Sigma P_0 Q_0} \times \frac{\Sigma P_1 Q_1}{\Sigma P_0 Q_0}} \times 100\)