Statistics and probability
What Are Statistics?
-Statistics is a form of mathematical analysis that uses quantified models, representations and synopses for a given set of experimental data or real-life studies.
- If the data set depends on a sample of a larger population, then the analyst can develop interpretations about the population primarily based on the statistical outcomes from the sample.
Mean
The mean is also known as the average of all the numbers in a given series. It is calculated by adding up all the data points in the series and then dividing those by the total number of data points.
Median
- The median is the middle of the set of numbers.
- Median is calculated by ordering all the data points from the series in ascending order and then picking out the middle data point from it.
Mode
The mode is calculated as the data point which occurs most frequently in a given series. In other words, it is the most common number in a dataset. Mathematically, there is no formula mode, as it just takes into account the most frequently occurring items from the list.
Range
the range of a set of data is the difference between the largest and smallest values.
Variance
Variance (σ2) in statistics is a measurement of the spread between numbers in a data set. That is, it measures how far each number in the set is from the mean and therefore from every other number in the set.
standard deviation
- The Standard Deviation is a measure of how spread out numbers are.
- Its symbol is σ
- it is the square root of the Variance .
Interquartile Range
The interquartile range (IQR) is a measure of variability, based on dividing a data set into quartiles. The values that divide each part are called the first, second, and third quartiles; and they are denoted by Q1, Q2, and Q3, respectively.
- Q1 is the “middle” value in the first half of the rank-ordered data set.
- Q2 is the median value in the set.
- Q3 is the “middle” value in the second half of the rank-ordered data set.
The formula for inter-quartile range is given below
- IQR=Q3−Q1
- Where,
IQR=Inter-quartile range
Q1 = First quartile
Q3 = Third quartile
Function of statistics
- Statistics helps in the proper and efficient planning of a statistical inquiry in any field of study
- Statistics helps in presenting complex data in a suitable tabular, diagrammatic and graphic form for easy and clear comprehension of the data.
- Statistics helps in drawing valid inferences, along with a measure of their reliability about the population parameters from the sample data.
- Statistics helps in drawing valid inferences, along with a measure of their reliability about the population parameters from the sample data.
probability
probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.
Formula for Probability
The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favourable outcomes and the total number of outcomes.
Probability of event to happen P(E) = Number of favourable outcomes/Total Number of outcomes
Examples and Solutions of probability
1) There are 6 pillows in a bed, 3 are red, 2 are yellow and 1 is blue. What is the probability of picking a yellow pillow?
Ans: The probability is equal to the number of yellow pillows in the bed divided by the total number of pillows, i.e. 2/6 = 1/3.
Rules of probability
Sampling Distribution
A sampling distribution is a probability distribution of a statistic obtained from a larger number of samples drawn from a specific population. The sampling distribution of a given population is the distribution of frequencies of a range of different outcomes that could possibly occur for a statistic of a population.
premutation
A premutation is a situation in which there are an excess number of repeats in a gene that is at risk of increasing in length during reproduction but which does not cause disease in the person with the excess number of repeats.
combination
A combination is a mathematical technique that determines the number of possible arrangements in a collection of items
Difference between premutation and combination
What is Analysis of Variance (ANOVA)?
Analysis of variance (ANOVA) is an analysis tool used in statistics that splits an observed aggregate variability found inside a data set into two parts: systematic factors and random factors.
The systematic factors have a statistical influence on the given data set, while the random factors do not.
Analysts use the ANOVA test to determine the influence that independent variables have on the dependent variable in a regression study.
The Formula for ANOVA is:
F=MSE/MST
where :F=ANOVA coefficient
MST=Mean sum of squares due to treatment
MSE=Mean sum of squares due to error