Statistical Techniques and Concepts

Statistics is the science of collecting, organizing , presenting, analyzing, and interpreting data to assist in making more effective decisions. Statistics can be divided into two broad areas:

Descriptive statistics and

Inferential statistics

Descriptive statistics are used to describe and summarize the properties of the mass of data collected from the respondents. Displays of data, such as histograms and box-plots, are also considered techniques of descriptive statistics.

Inferential statistics are used to infer the properties of the population from the properties of the sample. It consists of generalizing from samples to populations, performing estimations and hypothesis tests, determining relationships among variables, and making predictions.

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Frequency Distribution and Data Presentation

A frequency distribution is a table that displays the frequency of various outcomes in a sample. Each entry in the table contains the frequency or count of the occurrences of values within a particular group or interval, and in this way, the table summarizes the distribution of values in the sample. Organizing Data. 1.Arrange data into an array 2. Decide on the number of classes( k) 3. Calculate the class interval 4. Prepare a tally sheet There are two types of Frequency: Categorical frequency distribution. Grouped frequency distribution. Categorical Frequency Distributions The categorical frequency distribution is used for data that can be placed in specific categories or represent values of a qualitative variable. Grouped Frequency Distributions: When the data are numerical and their range is large, the data must be grouped into classes that are more than one unit in length. Histogram The histogram is an accurate graphical representati...

Mean, Median and Mode

Mean: A simple or arithmetic average of a range of values or quantities, computed by dividing the total of all values by the number of values. For example, the mean of 1, 2, 3, 4, and 5 is (15 ÷ 5) = 3. It is the most common and best general purpose measure of the mid-point (around which all other values cluster) of a set of values, but is prone to distortion by the presence of extreme values and may require the use of a measure of distortion (such as mean deviation or standard deviation). Also called arithmetic mean. Example 1: What is the Mean of these numbers? 6, 11, 7 · Add the numbers: 6 + 11 + 7 = 24 · Divide by how many numbers (there are 3 numbers): 24 / 3 = 8 Median: Value or quantity that falls halfway between a set of values arranged in an ascending or descending order. When the set contains an odd number of values, the median value is exac...

Probability

Probability is the measure of the likelihood that an event will occur. Probability is quantified as a number between 0 and 1, where, loosely speaking,0 indicates impossibility and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes (“heads” and “tails”) are both equally probable; the probability of “heads” equals the probability of “tails”; and since no other outcomes are possible, the probability of either “heads” or “tails” is 1/2 (which could also be written as 0.5 or 50%). Types of probability 1) Classical Probability – All sample points have equal chances of the event to happen. 2) Relative frequency- The probability of single data compared to the whole data i.e. possible event to happen relative to all the possible outcomes. 3) Subjectable -Individual, personal judgment to say the probability of t...

Priyanka Thakur

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