# Important Formulas in Statistics for Economics | Class 11

### Chapter: Organisation of Data

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

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

### Chapter: Diagrammatic Presentation of Data

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

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

OR

### Chapter: Measures of Central Tendency: Arithmetic Mean

#### 1. 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

#### 2. Charlier’s Accuracy Check

**For Short-cut Method**

âˆ‘f(d + 1) = âˆ‘fd + âˆ‘f

**For Step Deviation Method**

#### 3. Missing Value

**i) Individual Series:**

Where,

X_{1}, X_{2}, ………………… X_{n-1} = Given Values

X_{n} = Missing Value

**ii) Discrete Series:**

**iii) Continuous Series:**

#### 4. Combined Mean

Where,

N_{1} = Number of Items of first distribution

N_{2} = Number of Items of second distribution

#### 5. Corrected Mean

#### 6. Weighted Arithmetic Mean

Where,

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

âˆ‘W = Sum of the weights

### Chapter: Measures of Central Tendency: Median and Mode

#### 1. Median

Where,

N = Number of Items

**If the Number of Items is Even**

**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 class

c.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

#### 2. Quartiles

**i) Individual Series:**

Where,

N = Number of Items

**ii) Discrete Series:**

Where,

N = Cumulative Frequency

**iii) Continuous Series:**

#### 3. Mode

**i) Individual Series:**

Mode is the value which 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

= lower limit of the modal class

= frequency of modal class

f_0 = frequency of pre-modal class

= frequency of the next higher class or post-modal class

i = size of the modal group

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

Mode = 3 Median – 2 Mean

### Chapter: Measures of Dispersion

#### 1. Range

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

#### 2. Coefficient of Range

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

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

In **Continuous Series,** 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.

#### 3. Quartile Deviation

Where,

Q_{3} = Upper Quartile (Size of item)

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

#### 4. Coefficient of Quartile Deviation

Where,

Q_{3} = Upper Quartile (Size of item)

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

#### 5. 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 mean

âˆ‘f_{A} = Number of values below actual mean including actual mean

N = Number of Observations

**ii) Discrete Series:**

**Mean Deviation from Mean**

**Mean Deviation from Median**

Where,

M = Median

**iii) Continuous Series:**

**Mean Deviation from Mean**

**Mean Deviation from Median**

Where,

M = Median

#### 6. Coefficient of Mean Deviation

**Coefficient of Mean Deviation from Mean**

**Coefficient of Mean Deviation from Median**

#### 7. Standard Deviation

Where,

Ïƒ = Standard Deviation

âˆ‘x^{2} = Sum total of the squares of deviations from the actual mean

N = 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 deviations

N = Number of pairs of observations

**ii) ****Discrete Series****:**

Where,

Ïƒ = Standard Deviation

âˆ‘fx^{2} = Sum total of the squared deviations multiplied by frequency

N = 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 frequencies

N = 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 frequency

N = Number of pair of observations

Ïƒ =

Ïƒ = Standard Deviation

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

âˆ‘fd = Sum total of deviations multiplied by frequency

N = Number of pair of observations

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

#### 8. Coefficient of Standard Deviation

#### 9. 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

#### 10. Variance

Variance = Ïƒ^{2}

#### 11. Coefficient of Variation

Where,

C.V. = Coefficient of Variation

Ïƒ = Standard Deviation

= Arithmetic Mean

### Chapter: Correlation

#### 1. Degree of Correlation

#### 2. 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,

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 mean

âˆ‘dy^{2} = Sum of squared deviations of Y values from assumed mean

âˆ‘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

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

With Covariance formula, the formula for r (coefficient of correlation) can be written as:

Or,

Or,

Or,

#### 4. Spearman’s Rank Correlation Coefficient

**When ranks are not equal**

Where,

r_{k }= Coefficient of rank correlation

D = 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.

### Chapter: Index Number

#### 1. Unweighted or Simple Index Numbers

Where,

P_{01} = Index Number of the Current Year

âˆ‘p_{1} = Total of the current year’s price of all commodities

âˆ‘p_{0} = Total of the base year’s price of all commodities

#### 2. Weighted Index Numbers

**i) ****Weighted Aggregative Method**

Here,

P_{01} = Price Index of the current year

p_{0} = Price of goods at base year

q_{0} = Quantity of goods at base year

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

Here,

P_{01} = Price Index of the current year

p_{0} = Price of goods in the base year

q_{1} = Quantity of goods in the base year

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

Here,

P_{01} = Price Index of the current year

p_{0} = Price of goods in the base year

q_{1} = Quantity of goods in the base year

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

Fisher’s Method is considered the Ideal Method for Constructing Index Numbers.

**ii) ****Weighted Average of Price Relatives Method**

#### 3. Methods of Constructing Consumer Price Index

**Aggregate Expenditure Method**

**Family Budget Method**

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