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Statistics is mainly used to study quantitave research. It is used to organise and analyse data, to analyse percentage scores. Statistics enables us to serve two purposes namely description and pridiction. Descriptive statistics is used to study the distribution of data, pridiction is based on general forcasts.

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**Numerical variable**

** Example : **Age, height and weight of a person.

Outcomes in the roll of a die 1,2,3,4,5 and 6

**Categorical Variable**

** Example :** Hair color, nationality , status , position and the role of a person.

Outcomes in a toss of a coin head and tail

Discrete Variable: A numerical variable is said to be discrete if it assumes only countable or infinitely countable numbers.

Continuous Variable: Continuous variables take in all the values in an interval formed by two given numbers. Continuous variables are measured and not counted.

Random Variable: Random variable is a numerical variable whose value is determined by chance and it is used as a function to assign numerical values to the outcomes of a sample space.

While the discrete random variable assigns countable numbers to sample space elements, the continuous random variables assigns intervals on the number line to the outcomes.

Using the mapping ability of random variables even the non numerical outcomes of a sample space gets translated into numerical values and can be analytically treated. For example the two outcomes the head and tail of the simple experiment of tossing a coin can be translated into numerical values of 0 and 1 using the one-to-one mapping of random variable.

X = {0, 1, 2, 3}

Both the probabilities of turning a head and tail in a single throw = . Hence the probabilities of the compound events represented by the discrete variables 0,1,2 and 3 are as follows.

P(x=0) = x x =

P(x=1) =3 x x x =

P(x=2) =3 x x x =

P(x=3) = x x =

The discrete variables can be tabled along with the respective probabilities in a manner similar to a frequency distribution.

X |
0 | 1 |
2 |
3 |

P(X) |

This mapping of discrete random variables to their probabilities is called a probability function or probability distribution if the following conditions are met.

- P(x) 0 for all values of x in the range space
- The sum of all such probabilities = 1. i.e = 1.

Binomial and Poisson distributions are examples for discrete probability distributions. Binomial distributions are related to Bernoulli trials of two outcome probability experiment. The two outcomes in a single trial are defined as success and failure. The probabilities of these two complimentary events are used in calculating the probability function of the random variable. The expected value of a probability distribution is commonly known as the mean of the distribution. The parameters of a binomial distribution are ‘n’ and ‘p’ where n is the number of trials and p the probability of success in a single trial. The mean and standard deviation of the probability distribution are given by the formulas

mean = np and standard deviation = where q = 1-p, the probability of failure in a single trial.

Probability density function can be defined for a continuous random variable x, just as a probability distribution function is defined for a discrete variable.

A function f(x) is said to be the probability density function of a continuous random variable if the following conditions are met

f(x) 0 for all x

=1

Normal probability distribution with its bell shaped curve is a commonly known continuous probability distribution. Normal probability distribution is a symmetric distribution and the area under the curve for an interval represent the probability of the interval being the value of the variable. An area table for standardized normal distribution is used to find the required probabilities. The mean of the standard normal distribution is 0 and the standard deviation is 1.For this purpose the given variables are transformed into standardized normal variable, which is popularly known as z-score. The formula used for transforming a normal variable ‘x’ is as follows:

z= where is the mean and the standard deviation of the distribution under study.

- Sampling done using random methods.
- Determining the sample error expected.
- Estimating the population parameter using the sample statistic.
- Analyzing the estimates and drawing conclusion within the allowance of confidence levels.

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Help with Statistics tutorial is concerned with collection, analysis and explanation of data. Statistics help from Tutornext deals with learning the basic concepts which include finding mean, mode, median and variance from the collected data. Our online statistics tutors do their best to make the students get the best out of the online session. Not only tutoring, but also homework help can be availed whenever needed.

Help with Statistics tutoring is concerned with collection, analysis and explanation of data. Statistics help from Tutornext deals with learning the basic concepts which include finding mean, mode, median and variance from the collected data. Our online statistics tutors do their best to make the students get the best out of the online session. Not only tutoring, but also homework help can be availed whenever needed.

Choose your Statistics topic below:

Chapter 1: Introduction to Statistics

Chapter 2: Mean, Median and Mode

Chapter 3: Stem and Leaf Plots

Chapter 4:Bar Graphs

Chapter 5: Pie Charts

Chapter 6: Normal Distribution

Chapter 7:Data Handling

Chapter 8: Survey Sampling

Chapter 9: Regression and Regression Analysis