Statistics for Economics is a field that helps in the study, collection, analysis, interpretation, and organization of data for different ultimate objectives. Statistics help a user in gathering and analyzing huge numerical data easily and efficiently. For this, it provides various statistical tools and formulas that can be used to collect, interpret, and analyse the given set of data. Following are some of the important formulas (chapter-wise) used in Class 11^{th} Statistics for Economics.

## Table of Content

- 1. Width of Class Interval
- 2. Mid-Point or Mid-Value
- 3. Conversion of percentage into degrees in Pie Diagram
- 4. Adjustment Factor for any Class (Histogram)
- 5. Arithmetic Mean
- 6. Charlier’s Accuracy Check
- 7. Formula to calculate Missing Value in Individual, Discrete, and Continuous Series
- 8. Combined Mean
- 9. Corrected Mean
- 10. Weighted Arithmetic Mean
- 11. Median
- 12. Quartiles
- 13. Deciles
- 14. Percentiles
- 15. Mode
- 16. Relationship between Mean, Median, and Mode
- 17. Range
- 18. Coefficient of Range
- 19. Quartile Deviation
- 20. Coefficient of Quartile Deviation
- 21. Mean Deviation
- 22. Coefficient of Mean Deviation
- 23. Standard Deviation
- 24. Coefficient of Standard Deviation
- 25. Combined Standard Deviation
- 26. Variance
- 27. Coefficient of Variation
- 28. Degree of Correlation
- 29. Karl Pearson’s Coefficient of Correlation
- 30. Karl Pearson’s Coefficient of Correlation and Covariance
- 31. Spearman’s Rank Correlation Coefficient
- 32. Unweighted or Simple Index Numbers
- 33. Weighted Index Numbers
- 34. Methods of Constructing Consumer Price Index
- 35. Purchasing Power
- 36. Real Wages

**1. ****Width of Class Interval**

**1.**

**Width of Class Interval**

Where,

Largest Observation is the largest value of the given data set

Smallest Observation is the smallest value of thegiven data set

Number of Classes Desired is the number of class intervals required

**2. ****Mid-Point or Mid-Value**

**2.**

**Mid-Point or Mid-Value**

Where,

Lower Class Limit is the lower limit of a class interval of the given frequency distribution

Upper Class Limit is the upper limit of the same class interval of the given frequency distribution

## 3. Conversion of percentage into degrees in Pie Diagram

## 4. Adjustment Factor for any Class (Histogram)

OR

## 5. Arithmetic Mean

### i) Individual Series:

**Direct Method**

Where,

N = Total Number of Items

**Short-cut Method**

Where,

A = Assumed Mean

d = X – A (deviations of variables from assumed mean)

âˆ‘d = âˆ‘(X – A) (sum of deviations of variables from assumed mean)

N = Total Number of Items

**Step Deviation Method**

Where,

A = Assumed Mean

d = X – A (deviations of variables from assumed mean)

(Step Deviations; i.e., deviations divided by common factor)

C = Common Factor

N = Total Number of Items

### ii) Discrete Series:

**Direct Method**

Where,

âˆ‘fX = Sum of the product of variables with the respective frequencies

âˆ‘f = Total Number of Items

**Short-cut Method**

Where,

A = Assumed Mean

d = X – A (deviations of variables from assumed mean)

âˆ‘fd = Sum of the product of deviations (d) with the respective frequencies

âˆ‘f = Total Number of Items

**Step Deviation Method**

Where,

A = Assumed Mean

d = X – A (deviations of variables from assumed mean)

(Step Deviations; i.e., deviations divided by common factor)

C = Common Factor

âˆ‘f = Total Number of Items

### iii) Continuous Series:

**Direct Method**

Where,

âˆ‘fm = Sum of the product of mid-points with the respective frequencies

âˆ‘f = Total Number of Items

**Short-cut Method**

Where,

A = Assumed Mean

d = m – A (deviations of mid-points from assumed mean)

âˆ‘fd = Sum of the product of deviations (d) with the respective frequencies

âˆ‘f = Total Number of Items

**Step Deviation Method**

Where,

A = Assumed Mean

d = m – A (deviations of mid-points from assumed mean)

(Step Deviations; i.e., deviations divided by common factor)

C = Common Factor

âˆ‘f = Total Number of Items

## 6. Charlier’s Accuracy Check

**For Short-cut Method**

âˆ‘f(d + 1) = âˆ‘fd + âˆ‘f

Where,

f = Number of Observations

d = m – A (deviations of mid-points from assumed mean)

âˆ‘fd = Sum of the product of deviations (d) with the respective frequencies

âˆ‘f = Total Number of Items

**For Step Deviation Method**

Where,

f = Number of Observations

(Step Deviations; i.e., deviations divided by common factor)

C = Common Factor

A = Assumed Mean

âˆ‘f = Total Number of Items

## 7. Formula to calculate Missing Value in Individual, Discrete, and Continuous Series

### i) Individual Series:

Where,

X

_{1}, X_{2}, ………………… X_{n-1}= Given ValuesX

_{n}= Missing Value

### ii) Discrete Series:

Where,

âˆ‘fX = Sum of the product of variables with the respective frequencies

âˆ‘f = Total Number of Items

### iii) Continuous Series:

Where,

âˆ‘fm = Sum of the product of mid-points with the respective frequencies

âˆ‘f = Total Number of Items

## 8. Combined Mean

Where,

N

_{1}= Number of Items of first distributionN

_{2}= Number of Items of second distribution

## 9. Corrected Mean

## 10. Weighted Arithmetic Mean

Where,

âˆ‘WX = Sum of product of items and respective weights

âˆ‘W = Sum of the weights

## 11. Median

### i) Individual Series:

Where,

N = Number of Items

**If the Number of Items is Even**

Where,

N = Number of Items

### ii) Discrete Series:

Where,

N = Total of Frequency

Find out the value of Locate the cumulative frequency which is equal to higher than and then find the value corresponding to this cf. This value will be the Median value of the series.

### iii) Continuous Series:

Where,

l

_{1}= lower limit of the median classc.f. = cumulative frequency of the class preceding the median class

f = simple frequency of the median class

i = class size of the median group or class

## 12. Quartiles

### i) Individual Series:

Where,

N = Number of Items

### ii) Discrete Series:

Where,

N = Cumulative Frequency

### iii) Continuous Series:

## 13. Deciles

### i) Individual Series:

* *

……….

Where,

n is the total number of observations, D

_{1}is First Decile, D_{2}is Second Decile,……….D_{9}is Ninth Decile.

### ii) Discrete Series:

* *

……….

Where,

n is the total number of observations (âˆ‘f), D

_{1}is First Decile, D_{2}is Second Decile,……….D_{9}is Ninth Decile.

### iii) Continuous Series:

* *

……….

Where,

n is the total number of observations (âˆ‘f), D

_{1}is First Decile, D_{2}is Second Decile,……….D_{9}is Ninth Decile.

## 14. Percentiles

### i) Individual Series:

* *

……….

Where,

n is the total number of observations (âˆ‘f), P

_{1}is First Percentile, P_{2}is Second Percentile, P_{3}is Third Percentile, ……….P_{99}is Ninety Ninth Percentile.

### ii) Discrete Series:

……….

Where,

n is the total number of observations (âˆ‘f), P

_{1}is First Percentile, P_{2}is Second Percentile, P_{3}is Third Percentile, ……….P_{99}is Ninety Ninth Percentile.

### iii) Continuous Series:

……….

Where,

n is the total number of observations (âˆ‘f), P

_{1}is First Percentile, P_{2}is Second Percentile, P_{3}is Third Percentile, ……….P_{99}is Ninety Ninth Percentile.

## 15. Mode

### i) Individual Series:

Mode is the value that occurs the largest number of times.

### ii) Discrete Series:

In the case of regular and homogeneous frequencies, and single maximum frequency, Mode is the value corresponding to the highest frequency. Otherwise, the grouping method is used.

### iii) Continuous Series:

Where,

Z = Value of Mode

l

_{1}= lower limit of the modal classf

_{1}= frequency of modal classf

_{0}= frequency of pre-modal classf

_{2}= frequency of the next higher class or post-modal classi = size of the modal group

## 16. Relationship between Mean, Median, and Mode

Mode = 3 Median – 2 Mean

## 17. Range

Range(R) = Largest Item(L) – Smallest Item(S)

## 18. Coefficient of Range

In

the largest and smallest item is taken from the given observations.Individual Series,In

the largest and smallest item is taken from the given frequencies.Discrete Series,In

the first method to calculate coefficient of range is to take the difference between the upper and lower limit of the highest and lowest class interval respectively. The second method is to take the difference between the mid-points of the highest class limit and lowest class limit.Continuous Series,

## 19. Quartile Deviation

Where,

Q

_{3}= Upper Quartile (Size of item)Q

_{1}= Lower Quartile (Size of item)

## 20. Coefficient of Quartile Deviation

Where,

Q

_{3}= Upper Quartile (Size of item)Q

_{1}= Lower Quartile (Size of item)

## 21. Mean Deviation

### i) Individual Series:

**Mean Deviation from Mean**

**Mean Deviation from Median**

**Alternate Method**

Where,

âˆ‘|D| = Sum of absolute deviations from Assumed Mean

A = Assumed Mean

âˆ‘f

_{B}= Number of Values from actual meanâˆ‘f

_{A}= Number of values below actual mean including actual meanN = Number of Observations

### ii) Discrete Series:

**Mean Deviation from Mean**

**Mean Deviation from Median**

Where,

âˆ‘f|D| = Sum of product of frequency and absolute deviations from Assumed Mean

M = Median

N = Number of Observations

### iii) Continuous Series:

**Mean Deviation from Mean**

**Mean Deviation from Median**

Where,

âˆ‘f|D| = Sum of product of frequency and absolute deviations from Assumed Mean

m = Mid-value

M = Median

N = Number of Observations

## 22. Coefficient of Mean Deviation

**Coefficient of Mean Deviation from Mean**

Where,

= Mean Deviation from Mean

**Coefficient of Mean Deviation from Median**

Where,

MD

_{M}= Mean Deviation from MedianM = Median

## 23. Standard Deviation

### i) Individual Series:

Where,

Ïƒ = Standard Deviation

âˆ‘x

^{2}= Sum total of the squares of deviations from the actual meanN = Number of pairs of observations

Or

Where,

Ïƒ = Standard Deviation

âˆ‘X

^{2}= Sum total of the squares of observations= Actual Mean

N = Number of Observations

Where,

Ïƒ = Standard Deviation

âˆ‘d = Sum total of deviations from assumed mean

âˆ‘d

^{2}= Sum total of squares of deviationsN = Number of pairs of observations

### ii) Discrete Series:

Where,

Ïƒ = Standard Deviation

âˆ‘fx

^{2}= Sum total of the squared deviations multiplied by frequencyN = Number of pairs of observations

Or

Where,

Ïƒ = Standard Deviation

âˆ‘fx

^{2}= Sum total of the squared deviations multiplied by frequency= Actual Mean

N = Number of Observations

Or

Where,

Ïƒ = Standard Deviation

âˆ‘fd = Sum total of deviations multiplied by frequencies

âˆ‘d

^{2}= Sum total of the squared deviations multiplied by frequenciesN = Number of pairs of observations

Where,

Ïƒ = Standard Deviation

= Sum total of the squared step deviations multiplied by frequencies

= Sum total of step deviations multiplied by frequencies

N = Number of pairs of observations

### iii) Continuous Series:

Ïƒ =

OR

Where,

Ïƒ = Standard Deviation

= Actual Mean

âˆ‘fx

^{2}= Sum total of the deviations of every mid-value of the class intervals multiplied by frequencyN = Number of pair of observations

Ïƒ =

Where,

Ïƒ = Standard Deviation

âˆ‘fd

^{2}= Sum total of the squared deviations multiplied by frequencyâˆ‘fd = Sum total of deviations multiplied by frequency

N = Number of pair of observations

Where,

Ïƒ = Standard Deviation

= Sum total of the squared step deviations multiplied by frequency

= Sum total of step deviations multiplied by frequency

C = Common Factor

N = Number of pair of observations

## 24. Coefficient of Standard Deviation

Where,

Ïƒ = Standard Deviation

= Arithmetic Mean

## 25. Combined Standard Deviation

Where,

= Combined Standard Deviation of two groups

=Standard Deviation of first group

= Standard Deviation of second group

= Combined Arithmetic Mean of two groups

= Arithmetic Mean of first group

= Arithmetic Mean of second group

= Number of Observations in the first group

= Number of Observations in the second group

## 26. Variance

Variance = Ïƒ^{2}

Where,

Ïƒ = Standard Deviation

## 27. Coefficient of Variation

Where,

C.V. = Coefficient of Variation

Ïƒ = Standard Deviation

= Arithmetic Mean

## 28. Degree of Correlation

## 29. Karl Pearson’s Coefficient of Correlation

Or,

Or,

Or,

Or,

Where,

N = Number of Pair of Observations

x = Deviation of X series from Mean

y = Deviation of Y series from Mean

= Standard Deviation of X series

= Standard Deviation of Y series

r = Coefficient of Correlation

Where,

âˆ‘xy = Sum of Product of Deviation of X series and Y series from their respective Means

âˆ‘x

^{2 }= Sum of squares of Deviation of X Seriesâˆ‘y

^{2 }= Sum of squares of Deviation of Y Seriesr = Coefficient of Correlation

N = Number of Pair of Observations

Where,

âˆ‘XY = Sum of Product of X Series and Y Series

âˆ‘X = Sum of Series X

âˆ‘Y = Sum of Series Y

âˆ‘X

^{2 }= Sum of squares of Series Xâˆ‘Y

^{2 }= Sum of squares of Series Yr = Coefficient of Correlation

N = Number of Pair of Observations

Where,

N = Number of pair of observations

âˆ‘dx = Sum of deviations of X values from assumed mean

âˆ‘dy = Sum of deviations of Y values from assumed mean

âˆ‘dx

^{2}= Sum of squared deviations of X values from assumed meanâˆ‘dy

^{2}= Sum of squared deviations of Y values from assumed meanâˆ‘dxdy = Sum of the products of deviations dx and dy

Where,

N = Number of pair of observations

= Sum of deviations of X values from assumed mean

= Sum of deviations of Y values from assumed mean

= Sum of squared deviations of X values from assumed mean

= Sum of squared deviations of Y values from assumed mean

= Sum of the products of deviations and

## 30. Karl Pearson’s Coefficient of Correlation and Covariance

Where,

COV(X,Y) = Covariance of X and Y

âˆ‘xy = Sum of Product of Deviation of X series and Y series from their respective Means

N = Number of pair of observations

= Arithmetic Mean of Series X

= Arithmetic Mean of Series Y

## 31. Spearman’s Rank Correlation Coefficient

**When ranks are not equal**

Where,

r

_{k }= Coefficient of rank correlationD = Rank differences

N = Number of variables

**When ranks are equal**

Here,

m

_{1}, m_{2}, ……. are the number of times a value has repeated in the given X, Y, …….. series respectively.

## 32. Unweighted or Simple Index Numbers

Where,

P

_{01}= Index Number of the Current Yearâˆ‘p

_{1}= Total of the current year’s price of all commoditiesâˆ‘p

_{0}= Total of the base year’s price of all commodities

## 33. Weighted Index Numbers

### i) Weighted Aggregative Method

Here,

P

_{01}= Price Index of the current yearp

_{0}= Price of goods at base yearq

_{0}= Quantity of goods at base yearp

_{1}= Price of goods at the current year

Here,

P

_{01}= Price Index of the current yearp

_{0}= Price of goods in the base yearq

_{1}= Quantity of goods in the base yearp

_{1}= Price of goods in the current year

Here,

P

_{01}= Price Index of the current yearp

_{0}= Price of goods in the base yearq

_{1}= Quantity of goods in the base yearp

_{1}= Price of goods in the current yearFisher’s Method is considered the Ideal Method for Constructing Index Numbers.

### ii) Weighted Average of Price Relatives Method

Where,

âˆ‘RW = Sum of product of Price Relatives (R) and Value Weights (W)

âˆ‘W = Sum of Value Weights

## 34. Methods of Constructing Consumer Price Index

**Aggregate Expenditure Method**

Where,

p

_{1}= Price of goods in the current yearp

_{0}= Price of goods in the base yearq

_{0}= Quantity of goods at base year

**Family Budget Method**

Where,

âˆ‘RW = Sum of product of Price Relatives (R) and Value Weights (W)

âˆ‘W = Sum of Value Weights