# Basic Statistics

Basis statistics is a name for the body of scientific methods which are meant for collection of data , planning of the collection, analysis and interpretation of numerical data related to individuals or experiments.

We provide you with basic statistics tutorial. Students can get assistance through basic statistics tutorial. You can clear your doubts if you have any through this section. So, you can build up a strong conception by going through the basic statistics tutorial.

### Descriptive Statistics

Using Descriptive Statistics the basic and certain features of the data can be described. To analyze data we use both graphical analysis and descriptive statistics. If the data relates to a variable the process of summarization is done through Descriptive Statistics. There are two topics under descriptive statistics .They are described as follows:

### True Mean and Confidence Interval

A clear view and idea of raw data can be shown through descriptive statistics.. To meet that objective, a full range of indicators has been developed and you will find here after a definition of the most important ones. Mean is probably the most commonly used measure. It can be defined as the arithmetic average of all values.

### Confidence Interval

Confidence interval for a given sample is the range of values which includes the population parameter under consideration.

### Confidence Interval for Mean

Confidence limits for the mean are an interval estimate for the mean .Since we get different estimate of mean for different sample we prefer interval estimates. Interval estimates helps you to get an interval in which the true mean lies. A confidence interval is such an interval which tells you the upper and lower limit for mean. Such an interval estimate indicates the level of uncertainty in the estimate of mean, the more narrow the interval more accurate is the estimate, so wider the interval more the marginal error.90 %, 95 % , 99 % are the most commonly used intervals. It is to be noted that the confidence interval may contain the true mean. It may also happen sometimes that the interval does not contain the true mean. The confidence interval tells us the level of surety or confidence with which we are calculating it and not the probability that it contains the true mean. (1-α) ,the confidence coefficient is the proportion of samples that contain the true mean. The confidence interval tells you how sure you can be. For example the confidence interval for true mean µ is given by:

P[xbar -ta/2, n-1 * s/√n < µ < xbar +ta/2, n-1 * s/√n]=1-α

So the 100(1-α) % confidence limits to µ will be xbar -ta/2, n-1 * s/√n and xbar +ta/2, n-1 * s/√n, these being computed from the given sample.

### Sample Size and Confidence Interval

Larger sample size gives more precise idea about the population. So larger the sample size the more précised the results. So as we have already discussed earlier narrower the confidence interval the more precise the estimate, hence the larger the sample size the narrower the confidence interval and lesser the margin of error.

### Shape of The Normal Distribution, Normality

The normal distribution plays a very important role in statistical theory and its applications. A goodness of fit is measured to see how well the distribution fits to the data. Sometimes it is seen that the fit is not good and do not resemble normal distribution. For this you need to know about the shape of the normal distribution. Shape of the distribution is the shape of the probability distribution and is used to see how appropriate is the fit. There are various shape of distributions for example j-shaped U-shaped etc. Skewness and kurtosis are measures which are required to see whether the distribution fits the data. Since normal distribution is symmetric so skewness and kurtosis should not arise when you are fitting a normal distribution to your data. The Shape can be determined through quantitative measures like skewness ,kurtosis etc., or with the help of graphs such as histogram. Normality test determines the data set resembles a normal distribution or. Considerations of the shape of a distribution arise in statistical data analysis, where simple quantitative descriptive statistics and plotting techniques such as histograms can lead on to the selection of a particular family of distributions for modeling purposes. In statistics, normality tests are used to determine whether a data set is well-modeled by a normal distribution or not, or to compute how likely an underlying random variable is to be normally distributed.

Fig: Histogram for normal distribution:

### Basic Statistics Formulas

Students often require the basic statistics formulas for their study. We provide Basic Statistics Formula so that students can easily refer to it whenever they require them.

For further details in the descriptive section you can refer to elementary statistics concepts.

So, students can refer to our basic statistics section and in this way they can clear their doubts and misconceptions.

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