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Identify Functional Groups – 8 Practice Questions for Students and Cumulative Test (Full Atom Version)

Identify Each Functional Group (FULL ATOMS VERSION):      Functional groups can trip up any student who isn't paying close attention. Many functional groups look similar at a glance, but each has their own unique characteristics. Below are some functional groups that are commonly confused:     1) Amine VS Amide :           Amine:   Contains an NH₂ group.           Amide: Contains an  NH₂ group and a double-bonded oxygen on the same carbon. 👉 What is the difference between the two? An amide has a double-bonded oxygen; an amine does not. 2) Aldehyde VS Ketone:            Aldehyde: Has a double-bonded oxygen and a hydrogen attached to the same carbon, usually found at the end of a carbon chain.            Ketone: Has a double-bonded oxygen to a carbon that is connected to two other carbons, usually found in the middle of a...
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The Foundation: Types of Distributions


In statistics, there are a variety of distributions that are used under different circumstances. The goal of ALL distributions is to understand the population, usually by analyzing samples.

    In this section, we will break down probability distributions-- both theoretical and observational, discuss the two different types of data probabilities, and explore the subtle differences in specific distributions.


    Probability Distributions:

      Let's break it down into two sections:
        🔎 Distribution: A data spread of all observed values (real-world data).
        🔎 Probability: The theoretical likelihood of an outcome.
            👉 So, a probability distribution is the spread of all possible outcomes, each with its theoretical probability of occurring. No real-world data has been used.
     

    Theoretical versus Observational Data:

    A probability distribution is a general term to describe distribution of theoretical probabilities; however, once we start collecting real data we can describe it in two key ways: 

           🔎 Population distribution: The data collection from each individual within the population, or the target group.

           🔎 Sampling distribution: Several groups (of equal size n) are sampled. We collect the mean ("average") from each group to form the data. 

                    **n is just a placeholder for sample size-- it can be any number.



        Why do we care about sampling distributions?

                   Sampling is an faster and more cost efficient way to find the overall estimate of an entire population. Sampling is used in statistics when population data is difficult, time-consuming, or impractical to collect.

                        To learn more about the importance of sampling distributions: Link soon (We will explore CLT, calculations, and formulas).



After understanding the broad categories of distributions, we will look into two main types of distributions: discrete and continuous.


        🔎 Discrete: Countable numbers/outcomes.
                (1) the amount of people in a room 
                (2) the faces on a dice (1 through 6)
                (3) the sides of a coin (heads or tails)
                (4) the amount of times I cried taking statistics.

        🔎 Continuous: Infinite and uncountable numbers/outcomes.
                 (1) height
                 (2) temperature
                 (3) time (like 1.2 seconds, 1.23 seconds, etc.


     Discrete and continuous probability distributions have more SPECIFIC types of distributions:


             Discrete:


                🔎 Binomial: Two possible outcomes.
                        example: yes/no, success and failures, occurred/did not occur.

                🔎 Poisson: Counts how often an event occurs in a fixed interval of time or space; usually, Poisson distributions are used when events are rare.
                         example: the amount of ships sinking in a year.

            Continuous:  


                🔎 Normal: A bell-shaped distribution in which data is approximately distributed around a central value symmetrically.

                 🔎 Uniform: All outcomes are equally likely to occur.


            
NOTE: Distributions do not automatically determine the shape.


    
          

  
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