Statistics is defined as the area of mathematics that deals with data organisation, interpretation, analysis, and presentation. It is used extensively in many forms of commerce and scientific research so as to convert large datasets into usable insights. Here, in this blog, to make your learning journey easier, we will introduce you to some important basic statisticas formula.
In whatever area of study you may conduct investigation whether exploring or investigating trends, projecting or estimating future happenings, or making data-based decisions, probability and statistics simply cannot be done without.
Most students consider statistics a tough subject; however, it can be made easier once the basic statistical equations are comprehended.
Before getting into the formulas, allow me to share some thoughts on statistical vs. non-statistical statements.
Q1. At a Zoo, do owl monkeys typically weigh more compared to spider monkeys?
| (A) Statistical | (B) Not statistical |
Q2. At colleges in New York, do football coaches generally get paid higher as compared to tennis coaches?
| (A) Statistical | (B) Not statistical |
Q3. How many teeth does Alan have in the mouth?”
| (A) Statistical | (B) Not statistical |
Q4. How many days are in the month of July?
| (A) Statistical | (B) Not statistical |
Q5. What is the common area of giraffe ears?
| (A) Statistical | (B) Not statistical |
Q6. In general, what is the average height of the giraffes?
| (A) Statistical | (B) Not statistical |
Q7. Does Dev have a Ph.D. degree?
| (A) Statistical | (B) Not statistical |
Answers:–
- Statistical
- Statistical
- Not statistical
- Not statistical
- Statistical
- Statistical
- Not statistical
As you have checked your statistical knowledge, you can now proceed to check the basic statistics formulas. This will help you to solve statistical problems.
See also Tips on How to Learn Statistics More Effectively.
What is the purpose of using statistics?
Table of Contents
Table of Contents
Statistics is the study of the analysis, presentation, collection, interpretation, organization, analysis, and presentation of 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 the interpretation of several outcomes from it and the forecasting of various possibilities for upcoming applications. Several measurements of central data and the deviations of values that differ from the main values can be found with the use of statistics.
What are the elementary statistics formulas?
The fundamental idea and formulas of mean, mode, standard deviation, median, and variance serve as stepping stones for all statistical computations. Therefore, we have provided all the details on the basic statistics formula:
where,
x = Observations given
x(bar)= Mean
n = Total number of observations
Average or Mean
Theoretically, it is the sum of the components of a set that is divided by the total number of components.The concept of determining the mean is easily understandable. Thus, the formula of the 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.
See also Statistics for Economics: Its Benefits and Limitations
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 the median. On the other hand, if a particular set contains an even number of sets, then the two central values can be used to calculate the median.
The median can be used to distinguish the data set into two parts. To calculate the median, you have to arrange the components of the set in increasing order; only then can you 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
Below are some examples of basic statistics formulas that you should know:
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
See also What is Statistics Analysis & Where Can We Use it?
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 the 3rd term is the median of the data set.
If n is an even number
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
This means 2nd and 3rd terms 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 needs.
| Statistics Terms | Basic Statistics Formula |
| Percentile | Here is the sample mean, σ is the standard deviation, and n is the sample mean. |
| The margin of error for a sample mean | Here, Z* is the standard normal value, σis the sample size, and n is the standard deviation. |
| 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 mean | p = (p1 * n1 + p2 * n2) / (n1 + n2)Here, n1 and n2 are the sizes of sample 1 and sample 2, and p1 and p2 are the sample proportions taken from populations 1 and 2, respectively. |
| Correlation | Here, sx is the standard deviation of all the x values and sy is the standard deviation of all the x values. |
| Regression line | Y = 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 proportion | t = (x – μ) / SE. Here, μ is the hypothesized population mean, x is the standard error, and is the sample mean. |
| Chi-square statistics | Χ2 = [ ( n – 1 ) * s2 ] / σ2Here, a standard deviation is equal to σ, the sample is equal to s, and the sample of size n is from a normal population. |
| f statistic | s1^2/σ1^2 / s2^2/σ2^2These are the standard deviations of the data, σ1 and σ2.given population 1 and 2, s1 and s2 is the standard deviation of population 1 and 2, respectively. |
| One-sample t-test for means | Χ2 = 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. |
| Two-sample t-test for means | t = [ (x1 – x2) – d ] / SEHere, 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 statistics | μ = r / Here r is the number of successes, μ is the mean of trials, and P is the probability of success. |
| The Mean of the Negative Binomial Distribution | DF = k – 1K is the level of the categorical variable, and DF is the degree of freedom in this case. |
| Standard normal distribution | z = (X – μ) / σHere μ is the mean of X, X is a normal random variable, and σ is X’s standard deviation. |
| Chi-square goodness of fit test | μ = r / Here, r is the number of successes, μ is the mean of trials, and P is the probability of success. |
Conclusion
You can better grasp the fundamentals of statistics by reading this blog, which contains essential information on basic statistics formulas. Since there are other terminologies used in statistics, like variance, standard deviation, mean, median, mode, and so on, you can utilize the example above to work through any confusion you may have with these terms.
Even then, if you face any difficulty regarding the statistics assignments; then you can get the best statistics assignment help now. However, we have a team of experts who can provide you with help for your queries instantly, and we are available to you 24*7 and deliver plagiarism-free data before the deadlines along with the plagiarism report.
Frequently Asked Questions
Q1. How do you calculate basic statistics?
Some of the basic statistics formulas are:
1. Population standard deviation = σ = sqrt [ Σ ( Xi – μ )2 / N ]
2. Population mean = μ = ( Σ Xi ) / N.
3. Variance of population proportion = σP2 = PQ / n.
4. Population variance = σ2 = Σ ( Xi – μ )2 / N.
5. Standardized score = Z = (X – μ) / σ
Q2. Types of Statistics in Maths?
Statistics have majorly categorised into two types:
1. Descriptive statistics
2. Inferential statistics
