Correlation is a statistical tool which studies the relationship between two variables e.g. change in price leads to change in quantity demanded.
Correlation studies and measures the direction and intensity of relationship among variables. It measures co-variation not causation. It does not imply cause and effect relation.

An index number is a statistical device for measuring changes in the magnitude of a group of related variables.

Features of Index Number

1. Index numbers are expressed in terms of percentages. However, percentage sign (%) is never used.
2. Index numbers are relative measurement of group of data.
3. Index numbers offer a precise measurement of the quantitative change in the concerned variables over time.
4. Index number show changes in terms of averages.
5. They are expressed in numbers.
6. Index number facilitates the comparative study over different time period.

Firm. A firm is a single producing unit which produces goods and services for sale. Its main objective is to earn maximum profit.

Industry. An industry is an aggregate of all the firms producing the same product or interrelated product Alternatively, all the firms producing and selling the same or differentiated products of close substitutes are collectively known as an industry. For instance, firms manufacturing shoes will be collectively called shoe industry. Clearly a firm is a part of an industry.
Price determination. (Industry price-maker and firm price-taker). Under perfect competition, price of a commodity is determined by the equilibrium between market demand and market supply of the whole industry. So, the industry is called the price-maker. Here demand and supply represent total demand and total supply of industry. No individual firm can influence the price because its share in total supply is insignificant. Every firm has to accept the given price and adjust its level of output. It has no option but to sell the product at a price determined at industry level. If is because of this reason that firm is said to be price-taker and industry, the price-maker. This price is also called equilibrium price, because at this price quantity demanded is equal to quantity supplied. This can be illustrated with the help of the following demand and supply schedule and diagram of the industry:

A budget constraint represents all the combinations of goods and services that a consumer may purchase given current prices within his or her given income. Consumer theory uses the concepts of a budget constraint and a preference map to analyze consumer choices

An Economics tutor answered. Slope of a budget line is the "price ratio" of the two goods. ... Since the slope is constant we will get a straight line. The only case where a budget line may be non linear is the case of kinked constraints.

Univariate Frequency Distribution

1. When data is classified on the basis of single variable, the distribution is known as univariate frequency distribution.
2. It aims to make description about the particular variable.
3. It is also known as one-way frequency distribution.
4. Ex : Height of students in a class.

Bivariate Frequency Distribution :

1. When the data is classified on the basis of two variables, the distribution is known as bivariate frequency distribution.
2. It aims to determine the empirical relationship between the two variables.
3. It is also known as two-way frequency distribution.
4. Ex : Height and weight of students in a class.