#### Statistics Basic Concepts and types of Sampling

Basic definitions:

Statistics: It is the collection of techniques for planning the experiments, receiving data and then drawing the conclusions by organizing, summarizing, representing, analyzing, and interpreting.

Variable: It is the feature or characteristic which can suppose various values.

Random Variable: It is the variable who by chance determined the values.

Population: The study is the most common feature in population possessed by all subjects.

Sample: It is a subset or subgroup of all the population.

Parameter: It is the measure or feature which is obtained from the population.

Statistic (don’t confuse with Statistics): It is basically a feature or measure which is obtained from the sample.

Descriptive Statistics: It is nothing but the Collection, organization, summarization and the representation of data.

Inferential Statistics: The samples are generalized to populations by using the probability. Inferential Statistics perform the hypothesis testing, and it can make predictions by recognizing the relationships among variables.

Qualitative Variables: In this the non-numerical values are assumed by the variables.

Quantitative Variables: In this the numerical values are assumed by variables.

Discrete Variables: These are the variables usually obtained by counting and which suppose a countable or finite number of possible values.

Continuous Variables: These are the variables usually obtained by measurement and which suppose an infinite number of possible values.

Nominal Level: It is the level of measurement that categories data into mutually exclusive and in all inclusive categories no order or ranking can be imposed on data.

Ordinal Level: It is the level of measurement that ranked the categories which classifies the data. In this the differences between the ranks are not exist.

Interval Level: It is the level of measurement that can be ranked which is classified by data and where differences are meaningful. Though there is no meaningful zero, therefore the ratios are meaningless.

Ratio Level: It is the level of measurement that can be ranked by the classified data and where differences are meaningful and it consists of a true zero. In this, the true ratios exist between the various units of measure.

Random Sampling: The chance methods or random numbers are used for collecting the data.

Systematic Sampling: In this the data is obtained by selecting every kth object.

Convenience Sampling: In this the data which is used is readily available.

Stratified Sampling: It is the sampling in which the population is splitted into groups termed as strata. There are many other sampling techniques by which strata are sampled.

Cluster Sampling: Here the population is divided into splitted geographically. Some of such groups are arbitrarily chosen and then all the elements in such groups are chosen.

Population versus Sample:

Parameters are mainly related with the populations and statistics with samples. The population comprises all objects of interest while the sample is just a part of the population. The parameters are generally symbolized by using Greek letters (mu, sigma) whereas statistics are generally symbolized by using the Roman letters (x, s).

There are many reasons why we do not work with the populations. They are generally big, and it is frequently not possible to get data for each and every object. The more items surveyed the bigger cost as sampling doesn’t generally take place without cost.

We evaluate statistics and use them to estimate the parameters. Computation is the initial part of the statistics course and the estimation is the secondary part.

Discrete versus Continuous:

Discrete variables are generally obtained by the counting. While the continuous variables are generally obtained by measuring. Length, weight and time are all illustrations of continuous variables.

In Discrete variables, there are a countable or finite number of choices accessible with the discrete data. You can't enclose 2.63 people in the room. While continuous variables are the real numbers, we generally round them. This means a boundary based on the number of decimal places. For illustration: 64 is really anything 63.5 <= x < 64.5. Similarly, when there are two decimal places, then 64.03 is actually something 63.025 <= x < 63.035. The boundaries always contain one more decimal place than data and end in 5.

Levels of Measurement:

There are mainly four levels of measurement: Nominal, Ordinal, Interval and the Ratio. It goes from low level to high. The data is categorized according to the highest level that it fits. Any extra level just adds something in the previous one.

a) Nominal is the initial level. Here just names are meaningful.
b) Ordinal adds an order to names.
c) Interval adds up the meaningful differences
d) Ratio adds a zero and hence the ratios are meaningful.

Types of Sampling:

There are mainly five kinds of sampling which are described below:

1) Random sampling is analogous to place everyone's name into a hat and drawing out some names. Each and every element in the population has an equivalent chance of occurring. It is often difficult to prefer the way of sampling. Its main requirement is a complete list of every element in the population. Computer generated lists are frequently used with random sampling. By using the TI82 calculator we can produce random numbers.

2) Systematic sampling is much simpler to do in comparison to random sampling. In this the list of elements is ‘counted off’ that is, every kth element is taken. This is very much similar to lining everyone up and numbering off 1, 2, 3, 4, and so on.

3) Convenience sampling is much simple to do, however it is probably the worst method to use. Readily available data is mainly used here.

4) Cluster sampling is achieved by dividing the population to groups generally geographically. Such groups are termed as blocks or clusters. The clusters are arbitrarily chosen, and each element in the selected clusters is used.

5) Stratified sampling also splits the population into groups termed as strata. Though, this time, it is by some feature not geographically. For illustration, the population may be separated into females and males. The random, systematic or convenience sampling is either used for taking the strata.

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