Explore topic-wise InterviewSolutions in Current Affairs.

Statistical quality control (SQC) refers to the use of statistical methods in the monitoring and maintaining of the quality of products and services. This method is used to determine the tolerance limits for accepting a production process.

Seasonal Variations: As the name suggests, tendency movements are due to nature which repeats themselves periodically in every season. These variations repeat themselves in less than one year time. It is measured in an interval of time. Seasonal variations may be influenced by natural force, social customs, and traditions. These variations are the results of such factors which uniformly and regularly rise and fall in the magnitude. 

For example, selling umbrellas’ and raincoat in the rainy season, sales of cool drinks in the summer season, crackers in the Deepawali season, purchase of dresses in a festival season, sugarcane in Pongal season.

Cyclic Variations: These variations are not necessarily uniformly periodic in nature. That is, they may or may not follow exactly similar patterns after equal intervals of time. Generally, one cyclic period ranges from 7 to 9 years and there is no hard and fast rule in the fixation of years for a cyclic period. 

For example, every business cycle has a Start- Boom-Depression- Recover, maintenance during booms and depressions, changes in government monetary policies, changes in interest rates.

Irregular Variations: These variations do not have a particular pattern and there is no regular period of time of their occurrences. These are accidental changes that are purely random or unpredictable. Normally they are short – term variations, but its occurrence sometimes has its effect so intense that they may give rise to new cyclic or other movements of variations. 

For example, floods, wars, earthquakes, Tsunami, strikes, lockouts, etc…

Seasonal Index for every season (i.e) months, quarters, or year is given by 

Seasonal Index (S.I) = (Seasonal Average)/(Grand average) × 100 

Where seasonal average is calculated for month, (or) quarter depending on the problem, and Grand Average (G) is the average of averages.

The normal equations used in fitting a straight line are ΣY = na + b ΣX and ΣXY = a ΣX + b ΣX² 

Where n = number of years given in the data, 

X = time 

Y = actual value 

a, b = constants

Measurements of Trends 

The following are the methods by which we can measure the trend. 

1. Freehand or Graphic Method 

2. Method of Semi-Averages 

3. Method of Moving Averages 

4. Method of Least Squares

“An Index Number is a device which shows by its variations the Changes in a magnitude which is not capable of accurate measurements in itself or of direct valuation in practice”. – Wheldon 

“An Index number is a statistical measure of fluctuations in a variable arranged in the form of a series and using a base period for making comparisons” – Lawrence J Kalpana

Uses of Cost of Living Index Number 

•   It indicates whether the real wages of workers are rising or falling for a given time. 

•   It is used by the administrators for regulating dearness allowance or grant of bonus to the workers.

The uses of Index numbers are as given below: 

•  It is an important tool for formulating decisions and management policies. 

•  It helps in studying the trends and tendencies.

•  It determines the inflation and deflation in an economy

Family Budget Method: 

In this method, the weights are calculated by multiplying the prices and quantity of the base year. 

(i.e.) V = Σp₀ q₀ . The formula is given by, 

Cost of Living Index Number = ∑PV / ∑V

where P = P₁/P₀ x 100 is the price relative 

V = Σp₀q₀ is the value relative

Classification of Index Numbers: 

Index number can be classified as follows 

1. Price Index Number: It measures the general changes in the retail or wholesale price level of a particular or group of commodities. 

2. Quantity Index Number: These are indices to measure the changes in the number of goods manufactured in a factory. 

3. Cost of living Index Number: These are intended to study the effect of change in the price level on the cost of living of different classes of people.

Cost of Living Index Number is constructed to study the effect of changes in the price of goods and services of consumers for a current period as compared with the base period. The change in the cost of living index number between any two periods means the change in income which will be necessary to maintain the same standard of living in both the periods. Therefore the cost of living index number measures the average increase in the cost to maintain the same standard of life.

Further, the consumption habits of people differ widely from class to class (rich, poor, middle class) and even with the region. The changes in the price level affect the different classes of people, consequently, the general price index numbers fail to reflect the effect of changes in their cost of living in different classes of people. Therefore, the cost of living index number measures the general price movement of the commodities consumed by different classes of people.

The ratio between the total value of the current period and the total value of the base period is known as the true value ratio. 

(i.e) true value ratio = ∑p₁q_1 / ∑p₀q₀

The weighted aggregate index number using base period weights is called Laspeyre’s price index number.

\(P^L_{01} = \frac {\sum p_1q_0} {\sum p_0q_0}\times100\)

Where p₁ is current year price 

p₀ is base year price 

q₀ is base year quantity

Laspeyres Index is a methodology to calculate the consumer price index by measuring the change in the price of the basket of goods to the base year.

Its relationship is given as:

Laspeyres Index Formula= ∑ ( Observation Price * Base Qty) / ∑ ( Base Price * Base Qty)

If both prices and quantities were permitted to change, then it is impossible to isolate the part of movement due to price changes alone. In this case, the current year quantities appear more realistic weights than the base year quantities. The index number based on current year quantities is called Paasche’s price index number.

\(P^P_{01} = \frac {\sum p_1q_0} {\sum p_0q_0}\times100\)

Where p₁ is the current year price 

q₁ is the current year quantity 

p₀ is the base year price

Index numbers are studied to know the- relative changes in price and quantity for any two years compared. There are two tests that are used to test the adequacy for an index number. The two tests are as follows 

•  Time Reversal Test 

•  Factor Reversal Test 

The criterion for a good index number is to satisfy the above two tests.