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UNIT-3

CHAPTER-2

STATISTICS

• Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. The science of collecting, organizing, presenting, analyzing, and interpreting data to assist in making more effective decisions.
• Statistical analysis – used to manipulate summarize and investigate data, so that useful decision-making information
• Finding average values of some values of some variable: Statistical methods help in finding average values of variables. Sometimes it is necessary to know average values like average land price of a particular location etc.
• Market Survey: Statistical sampling methods are used for market survey which is very much important for decision making………….

MEAN VS MEDIAN

Both are measures of where the center of a data set lies (called “Central Tendency” in stats), but they are usually different numbers. For example, take this list of numbers: 10, 10, 20, 40, 70.

The mean (informally, the “average“) is found by adding all of the numbers together and dividing by the number of items in the set: 10 + 10 + 20 + 40 + 70 / 5 = 30.

The median is found by ordering the set from lowest to highest and finding the exact middle. The median is just the middle number: 20.

Sometimes the two will be the same number. For example, the data set 1, 2, 4, 6, 7 has a mean of 1 + 2 + 4 + 6 + 7 / 5 = 4 and a median (a middle) of 4.

MEAN VS AVERAGE: WHAT’S THE DIFFERENCE?

When you first started out in mathematics, you were probably taught that an average was a “middling” amount for a set of numbers. You added up the numbers, divided by the number of items you can and you get the average. For example, the average of 10, 6 and 20 is:

10 + 6 + 20 = 36 / 3 = 12.

The you started studying statistics and all of a sudden the “average” is now called the mean. What happened? The answer is that they have the same meaning(they are synonyms) That said, technically, the word mean is short for the arithmetic mean. We use different words in stats, because there are multiple different types of means, and they all do different thing. Specific “Means” commonly used in Stats You’ll probably come across these in your stats class. They have very narrow meanings:

Mean of the sampling distribution: used with probability distributions, especially with the Central Limit Theorem. It’s an average of a set of distributions.

MEAN

• Is the average of a group of numbers
• Applicable for interval and ratio data, not applicable for nominal or ordinal data

• Affected by each value in the data set, including extreme values

• Computed by summing all values in the data set and dividing the sum by the number of values in the data set

The mean formula is defined as the sum of the observations divided by the total number of observations. This will be helpful in solving a majority of the topics related to the arithmetic mean. The mean formula of given observations can be expressed as,

Mean Formula = (Sum of Observations) ÷ (Total Numbers of Observations)

Similarly, we have a mean formula for grouped data. Which is expressed as x̄ = Σfx/N

Where,

• x = the mean value of the set of given data.
• f = frequency of the individual data
• N = sum of frequencies

Hence, the average of all the data points is termed as mean.

PART-V

INDEX NUMBERS

Index numbers are devices, which indicate by its variations the changes in the magnitude in a group of related variables. The group of related variables may be the prices of a specified set of commodities or the volume of production in different sectors or such other concept as intelligence, health or efficiency. They may measure variations over time, over space or between similar categories such as institutions, object, etc.

Price index number is the most used, measuring variation in prices over a span of time enabling to know the change of price level of group of commodities at certain periods of time as compared to another period called base period. Thus it involves prices over two different periods. When the price of one commodity rise while the price of another falls and the prices of various commodities all react in different degrees, the index number shall not give here any indication of changes in the values of the individual commodity but reveals the average net effect o all the changes. Retail price index (R.P.I), wholesale price e.. ……………………….READ MORE

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