basic statistics formula

A Definitive Guide on The Basic Statistics Formula

Most of the students finding it difficult to learn statistics. But here are some basic statistics formula that can help the students to get started with statistics. But before we are going to learn these formulas. Let’s start with the introduction to statistics.

Statistics is one of the branches of mathematics that is used to study the analysis of the data. The methods of statistics are generated to examine the large data and their properties.

Statistics formulas are used by several companies to calculate the report of the people or employees. In the upcoming paragraphs, we will discuss several statistical formulae that are used for different purposes.

Before proceeding to the basic statistics formulas; let’s check whether you can analyze which is a statistical statement and which is a non-statistical statement.

At a Zoo, do owl monkeys typically weigh more as compare to spider monkeys?
(A) Statistical(B) Not statistical
At colleges in New York, do football coaches generally get paid higher as compared to tennis coaches?
(A) Statistical(B) Not statistical
How many teeth does Alan have in the mouth?”
(A) Statistical(B) Not statistical
How many days are in the month of July?
(A) Statistical(B) Not statistical
What is the common area of giraffe ears?
(A) Statistical(B) Not statistical
In general, what is the average height of the giraffes?
(A) Statistical(B) Not statistical
Does Dev have a Ph.D. degree?
(A) Statistical(B) Not statistical

Answers

1Statistical
2Statistical
3Not statistical
4Not statistical
5Statistical
6Statistical
7Not statistical

As you have checked your statistical knowledge, now you can proceed to check the basic statistics formulas. This will help you to solve statistical problems.

What is the purpose of using statistics?

Table of Contents

Statistics is the study of the analysis, presentation, collection, interpretation, and organization, analysis, and presentation of the large data. It can be defined as a function of the given data. That is why statistics are combined with classifying, presenting, collecting, and arranging the numerical information in some manner. It also facilitates to interpret several outcomes from it and forecast various possibilities for the upcoming applications. With the help of statistics, one can find several measures of central data and the deviations of dissimilar values from the main values.

What are the elementary statistics formulas?

For all the statistical computations, the basic concept and formulas of mean, mode, standard deviation, median, and variance are the stepping stones. Therefore, we have provided all the details on basic statistics formula:

Average or Mean

Theoretically, it is the sum of the components of a set that is divided by the total number of components. You can easily understand the whole concept of calculating the mean. Thus, the formula of mean is:

Mean = (sum of all the given items) / total no. of items

The ability of the mean is used to show the overall dataset with a single value.

Median

It is the central value of the overall dataset. But if a set has an odd number of values, then the central value of the set can be considered as the median. On the other side, if a particular set contains even no. of the sets, then the two central values can be used to calculate the as the median.

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The median can be used to distinguish the data set into two different parts. To calculate the median, you have to arrange the components of the set in increasing order; only then you can find the median of the data. 

Median = (n+1)/2 ; where n is odd number

Or

Median = [(n/2) term + ((n/2) + 1)] /2 ; where n is the even number

These are the basic statistics formula to calculate the median of the given data.

Mode

It is the value that is frequently used in a single dataset. Or we can say that mode is the summary of the dataset with a single data.

Mode = Frequently used data in a given set

Variance

It is used for calculating the deviation of a data set by its mean value. Therefore, it must be a positive value, and it is also used to measure the value of the standard deviation, which is considered as the essential concept of the statistics values.

Where is variance; x = given items; x bar = mean; and n = total no of itmes

Standard Deviation

It is the square root of the variance of the given information.

S =

Where S = Standard deviation and is the square root of the variance.

Some of the examples of basic statistics formula

  • Mean: Find the mean of the data 1,2,3,4,5.

As Mean = (sum of all the given items) / total no. of items

Therefore, mean = (1+2+3+4+5)/5

15/5 =3

Hence, the mean = 3

  • Median: If n is an odd number:

Find the median of the data 10,20,30,40,50.

Then, the median can be calculated by writing the data set in ascending order, i.e.

10,20,30,40,50

Therefore, 30 is the median, as it is the central value of the data set.

Or Median = (n+1)/2 ;

Where n=5, therefore (5+1)/2 = 3,which means 3rd term is the median of the data set.

If n is even number

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Find the median of the data 4,10,15,2.

Then, the median can be calculated by writing the data set in ascending order, i.e.

2,4,10,15

Now, the median is calculated by Median = [(n/2) term + ((n/2) + 1)] /2 ; therefore,

[(4/2) + (4/2)+1)]/2 = 2.5

Which means 2nd and 3rd term will be used for median i.e.

(4+10)/2 = 7. The median is 7.

  • Mode: Find the mode of the data 1,1,2,2,2,3,3,3,3,4,4.

As 3 is repeated 4 times; therefore, the mode of the data is 3.

  • VarianceFind the variance of the data 10,5,-6,3,12.

Therefore, the sigma (variance) can be calculated as [(10)^2 + (5)^2 + (-6)^2 + (3)^2 + (12)^2]/5

[100+25+36+9+144]/5 = 62.8

The variance is 62.8.

Standard deviation

In the above example, we have calculated the variance of the data. Now, using the value of the variance, we can calculate the standard deviation.

S = √ (variance)

S = (62.8)

= 7.92

Therefore, the standard deviation is 7.92.

List of other important statistics formulas

Below, we have mentioned some of the important statistics formulae. Students can use any of them as per their need.

Statistics TermsBasic Statistics Formula
PercentileConvert the original formula into the standard form with the help of z-formula. Then, use Z -table to solve it.
Here, x is the original value, image5.pngis the population mean, and σ is the standard deviation.
The margin of error for a sample mean Here,  Z* is the standard normal value, σ is the standard deviation, and n is the sample size.
Sample size Here,  Z* is the standard normal value, σ is the standard deviation, and MOE is the margin of error.
The test statistic for the meanHere,  is the sample mean, σ is the standard deviation, and n sample mean.
CorrelationHere, sx is the standard deviation of all the x values and sy is the standard deviation of all the x values.
Regression lineY = Β0 + Β1XHere, Β0 is a constant, X is the independent variable value, Β1 is the regression coefficient, and Y is the dependent variable’s value.
Pooled sample proportionp = (p1 * n1 + p2 * n2) / (n1 + n2)
Here, n1 and n2 is the size of sample 1 and sample 2, p1 and p2 are the sample proportion taken from population 1 and 2 respectively.
Chi-square statisticsΧ2 = [ ( n – 1 ) * s2 ] / σ2
Here, a standard deviation equal to σ, the sample is equal to s, and the sample of size n from a normal population.
f statistics1^2/σ1^2 / s2^2/σ2^2
Here, σ1 and σ2 are the standard deviations of the given population 1 and 2, s1 and s2 is the standard deviation of population 1 and 2, respectively.
One-sample t-test for meanst = (x – μ) / SE, 
Here, μ is the hypothesized population mean, x is the sample mean, and SE is the standard error.
Two-sample t-test for meanst = [ (x1 – x2) – d ] / SE
Here, x1 and x2 is the mean of sample 1 and 2, SE is the standard error, d is the hypothesized difference among population means.
Chi-square test statisticsΧ2 = Σ [ (Oi – Ei)2 / Ei ]
Here Oi is the observed frequency count, and Ei is the expected frequency count that is used for the ith level of the categorical variable.
The Mean of the Negative Binomial Distributionμ = r / P
Here r is the number of successes, μ is the mean of trials, and P is the probability of success.
Standard normal distributionz = (X – μ) / σ
Here μ is the mean of X, X is a normal random variable, and σ is X’s standard deviation.
Chi-square goodness of fit testDF = k – 1
Here, DF is the degree of freedom, and K is the categorical variable’s levels.

Conclusion

This blog has relevant information on basic statistics formulas that can help you to understand the basic concept of statistics. As the statistics have different terminologies such as mean, median, mode, variance, and standard deviation, you can use the above-mentioned example to solve the problem of these statistical terms.

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Frequently Asked Questions

How do you calculate basic statistics?

Some of the basic statistics formulas are:
 
Population standard deviation = σ = sqrt [ Σ ( Xi – μ )2 / N ]
Population mean = μ = ( Σ Xi ) / N.
Variance of population proportion = σP2 = PQ / n.
Population variance = σ2 = Σ ( Xi – μ )2 / N.
Standardized score = Z = (X – μ) / σ

What is the formula for sample?

n = N*X / (X + N – 1), 
 
where X = Zα/22 *p*(1-p) / MOE2, and Zα/2 is the Normal distribution’s critical value at α/2, p is the sample proportion, MOE is the margin of error, and N is the size of the population.

What are the 2 fields of statistics?

The statistics are divided into two different parts: inferential and descriptive. Each of the parts is important, providing various techniques that are used to achieve diverse objectives.