Elementary Statistics

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Here are some interesting pointers 🙂

  • Statistics is one of the ancient branches of Mathematics. The history of statistics began as early as around 3500 years before Jesus Christ’s birth in Egypt.
  • Earlier, statistics were used by cattle or sheep owners to find out the amount of crop produced and the number of people living in a particular city.
  • As per history, it was also used by the Roman emperors to record the population and calculate taxes.
  • After several years, statistics began with an English Tradesman, John Graunt. Statistics are used to record and predict employment, inflation, population, etc.

What are Elementary Statistics?

Elementary Statistics is a mathematics branch that studies collecting, organizing, analyzing, interpreting, and presenting data or information.

For example, one can use elementary statistics to collect data on the women of different age groups in the city, marks obtained by a particular student etc.

Two Fields of Statistics

Descriptive Statistics

Descriptive statistics is a method of collecting, organizing, and presenting data in a way that describes or accesses the characteristics of a group.

Inferential Statistics

Inferential statistics aims to draw conclusions about populations based on the pre-selected elements.

List of Topics in Elementary Statistics

Here is a list of all the topics concerning elementary statistics:

  • Bar Graph
  • Bayes Theorem
  • Binomial Distribution
  • Box and Whiskers Plot
  • Conditional Probability
  • Central Limit Theorem
  • Chi-Square Distribution
  • Cluster Sampling
  • Coefficient of Determination
  • Combinations and Permutations
  • Confidence Intervals
  • Contingency Tables
  • Continuous Distributions
  • Correlation and Covariance
  • Dependent t-test for Matched Pairs
  • Discrete Distributions
  • F-Distribution
  • Frequency Distributions
  • Goodness of Fit Test
  • Histograms
  • Hypergeometric Distribution
  • Hypothesis Testing
  • Inferential Statistics
  • Interval Level of Measurement
  • Joint and Marginal Probability
  • Kruskall-Wallis Test
  • Levels of Measurement
  • Linear Regression
  • Line Graph
  • Measures of Variations
  • Multiple Regression
  • Mann-Whitney Test
  • Mean, Median, and Mode
  • Nominal Level of Measurement
  • Nonparametric Statistics
  • Normal Distribution
  • Normality
  • Ordinal Level of Measurement
  • Paired Wilcoxon Signed Rank Test
  • Parametric Statistics
  • Parameter
  • Population
  • Power of a Test
  • Poisson Distribution
  • P-Value
  • Ratio Level of Measurement
  • Quantitative and Qualitative Data
  • Quartiles
  • Range
  • Runs Test
  • Sample
  • Scatter Plots
  • Sign Test
  • Simple Random Sampling
  • Skewness
  • Standard Deviation and Variance
  • Standard Normal Distribution
  • Spearman’s Rank Correlation Coefficient
  • Stratified Sampling
  • Systematic Random Sampling
  • T-Distribution
  • Types of Sampling
  • Uniform Distribution
  • Wilcoxon Signed Ranks Test
  • Z-Test vs. T-test

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Few Important Topics in Elementary Statistics

Statistics being a vast subject, comprises a vast number of topics. Here are a few selected topics you can find in elementary statistics:

Mean, Median and Mode

Mean is another name for the arithmetic mean of the supplied data. If data are grouped and arranged in ascending order, the median is the middle value in the set of grouped data. The most frequent value in the data is called the mode.


ANOVA stands for Analysis of Variance. It is a statistical analysis technique that divides the observed aggregate variability into a data set into two parts: systematic and random factors. It is used to evaluate the impact of independent factors on the dependent variable in a regression analysis.

Bayes Theorem

Using the Bayes theorem, you can predict how likely any condition will lead to a particular event. It is also taken into account in the case of conditional probability.

  • The Bayes theorem is frequently referred to as the probability of “causes” formula.
  • Suppose we have to calculate the probability of selecting a blue marble from the second of three marble baskets, including three marbles of different colors, such as red, blue, and black.
  • Conditional probability is when other factors determine the likelihood of an event occurring.

Binomial Distribution

The binomial distribution is the discrete probability distribution used in probability theory and statistics that only allows for Success or Failure as the possible outcomes of an experiment. For example, if we flip a coin, there are only two conceivable results: heads or tails, and if we take a test, there are only two possible outcomes: pass or fail.

Chi-square Distribution

An extended family of continuous probability distributions is the chi-square (X2) family. They are frequently used in hypothesis tests, such as the chi-square test of independence and the goodness of fit test. Chi-square distributions are determined by k, a parameter where k is the number of degrees of freedom.

Cluster Sampling

Cluster sampling, commonly referred to as one-stage cluster sampling, is a method that identifies and includes groups of individuals who best represent the population in the sample [1]. This approach is frequently used when performing marketing research. Cost reduction and increased sampling efficiency are the main goals of cluster sampling.

Goodness of Fit Test

A statistical hypothesis test called “Goodness-of-Fit” evaluates how closely observed, and predicted data match each other. The results of goodness-of-fit tests can be used to establish whether a sample is distributed normally, whether categorical variables are connected, or whether random samples come from the same distribution. A goodness-of-fit test is used to determine if observed data lines up with expectations. We can make decisions based on the outcome of the hypothesis test conducted.

Hypothesis Testing 

In statistics, hypothesis testing is a method for determining if survey or experiment results are relevant. By calculating the likelihood that your results occurred by chance, you are determining whether your results are genuine. Your experiment won’t be repeatable and therefore won’t be of much help if your results could have happened by accident. Types of hypothesis testing:

  • Hypothesis Testing for One Mean
  • Hypothesis Testing for One Proportion
  • Hypothesis Testing for Two Means
  • Hypothesis Testing for Two Proportions
  • Hypothesis Testing for Variances

Who can help you with elementary statistics homework?

With this, you have understood that dealing with statistics is not simple. It needs a lot of knowledge and experience to complete elementary statistics homework. If you need elementary statistics homework help, we would love to suggest the Assignment Store. It is the leading online tutoring firm that offers you:

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