Basic Concepts of Statistics #2

This post is a continuation of the Basic concepts of Statistics. Click here for part 1.

In part 1 we learned the definitions of mean median and mode. In this post we will learn some additional concepts of statistics and basic terms.

Variance

Variance is a term that defines the range of values that may occur away from the mean of the sample. For example, you pick a random sample of 50 from 100 packets of chips and weigh them. You calculate the mean of that sample. Now if you repeat the experiment multiple times with picking the packets at random. you will find that the mean weight of each random sample falls within the range of variance. Variance is calculated in 3 steps.

variance formula - basic concepts of statistics

This is the formula for variance in basic statistical studies. The formula changes form as we go into advanced topics like random variables and probability distributions.

Standard Deviation

Standard deviation is the dispersion of values away from the mean in a sample or population. if the standard deviation is small compared to the mean then the values are closer to each other. If the standard deviation is large as compared to the mean then the values have a larger range of dispersion. The standard deviation has a simple formula.

std dev formula. basic concepts of statistics

Standard Error

In many statistical studies, there is no direct sample with data available. there is only information received from a source about the mean, variance and standard deviation of the population. In such cases, the observer needs to get an estimate of the standard deviation of the sample. Standard error is calculated using the formula

s is the standard deviation of the population. and n is sample size.

Note that the value of the standard error is inversely proportional to the sample size. This means that when we increase our sample size, our standard error is reduced. This tells us that we will be closer to the actual value of the standard deviation as we increase the sample size.

Proportion

A proportion is the part of the population, or sample, that shows the desired result of any statistical study. Proportional studies are mostly done for binary studies. That is studies that are Yes or no, like or dislike, support or obstruct. A Proportion is given by the following formula.

x is the number of points in the sample with desirable qualities. n is sample size

For example, A study was conducted in a school to find the proportion of students liking a new movie. 100 students were randomly selected and asked if they liked it. 65 reported that they did. This makes the proportion of students liking the movie P = 65/100 = 0.65 . Proportions are displayed as percentage values in the results of such studies. The result of this study will be stated as: 65% students liked a movie.

Surveys are the most popular in this regard. Movie reviewing websites like rotten tomatoes show us the proportion as results. Political polls also heavily rely on studies that give out results in proportions. The president’s approval ratings are shown every 3 months or after every major decision taken by the Government, in the USA.

Probability

Probability is defined as the likelihood of an occurrence of a desired event. This is the simplest definition of probability. For example if we look at coin tossing, then we can have heads or tails as outcomes. This tells us that probability of heads is 0.5 or 50%. So if we make a coin tossing experiment and toss a coin 200 times. we can expect 100 of these tosses to land as heads.

As we dive deeper into the topic of Probability we will encounter some basic concepts of probability as well. To learn more about Probability Click here.

Distribution

A distribution in statistics is a mathematical function. This function follows a mathematical curve that can define the frequency of all possible values, that are part of a population. There are multiple know distributions that are frequently encountered in statistical studies. Normal distribution, exponential distribution, Poisson distribution and T distribution are the most common.

These are the basic concepts of statistics that one must be familiar with, before working in statistics.

Next: Introduction to Basic Probability #1

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