In measures of dispersion, the standard deviation is one of the prominent tools to calculate the dispersion of the data
In measures of dispersion, the standard deviation is one of the prominent tools to calculate the dispersion of the data
In measures of dispersion, the standard deviation is one of the prominent tools to calculate the dispersion of the data. The purpose of standard deviation is to calculate the deviation of data from the mean of the data. We first calculate the mean of the data, then we sum up the squared difference of each point from the mean.
Let’s directly start with an example of a simple series
34 34 40 43 45 46 48 46
The formula for a standard deviation for Simple Series is as follows, σ is Standard Deviation.
In this equation,
N is the number of items in a series, d2 is the Squared differences of items from the series mean
x | d=| x – μ | | d2 |
---|---|---|
34 | 8.5 | 72.25 |
38 | 4.5 | 20.25 |
40 | 2.5 | 6.25 |
43 | 0.5 | 0.25 |
45 | 2.5 | 6.25 |
46 | 3.5 | 12.25 |
48 | 5.5 | 30.25 |
46 | 3.5 | 12.25 |
Σx=340 , μ = 42.5 | Σd2= 160 |
From the above example, we get an idea of how the standard deviation works in theory and practice. As this is a simple series of data, we directly calculated the difference and deviations.
Although, we also face datasets of multiple types, like continuous and discrete series.
The series below is a discrete series. This type of data can be explained with x as the value or price and f as the frequency of x’s occurrence.
Let’s say x is the value of an item ordered from a grocery store, and f will be how many units of item x are ordered.
The apples cost $60, and there are 250 apples. So the fx will be, 15000
χ | ƒ |
60 | 250 |
62 | 300 |
64 | 410 |
66 | 500 |
67 | 350 |
68 | 275 |
69 | 150 |
70 | 100 |
71 | 25 |
f=2360 |
The calculations in this table for standard derivation are slightly different from the simple series. But the root of the formula is still the same.
χ | ƒ | ƒχ | d=| χ – μ | | d2 | ƒd2 |
---|---|---|---|---|---|
60 | 250 | 15000 | 5.3 | 28.09 | 7022.5 |
62 | 300 | 18600 | 3.3 | 10.89 | 3267 |
64 | 410 | 26240 | 1.3 | 1.69 | 692.9 |
66 | 500 | 33000 | 0.7 | 0.49 | 245 |
67 | 350 | 23450 | 1.7 | 2.89 | 1011.5 |
68 | 275 | 18700 | 2.7 | 7.29 | 2004.75 |
69 | 150 | 10350 | 3.7 | 13.69 | 2053.5 |
70 | 100 | 7000 | 4.7 | 22.09 | 2209 |
71 | 25 | 1775 | 5.7 | 32.49 | 812.25 |
Σƒ=2360 | Σƒχ=154115 | Σƒd2=19318.4 |
Let’s learn to calculate standard deviation from continuous data. In the following example, we will take a sample of continuous data and apply the standard deviation formula on it.
An example of continuous data can be stocks of a company throughout each month of a year, or the average/cumulative weight of students in a class.
The following example of Classes of IQs and f is the number of students in those classes of IQs
Class | F |
---|---|
40-50 | 11 |
50-60 | 23 |
60-70 | 40 |
70-80 | 60 |
80-90 | 35 |
90-100 | 16 |
100-110 | 09 |
110-120 | 06 |
The formulae for standard deviation are
The First Equation calculates the mean of the series.
The second equation calculates the difference between series and mean.
The third equation calculates standard deviation.
Class | Frequency f | Mid-value m | fm | d=|m-μ | μ=74.95 | d2 | fd2 |
---|---|---|---|---|---|---|
40-50 | 11 | 45 | 495 | 29.95 | 897 | 9867 |
50-60 | 23 | 55 | 1265 | 19.95 | 398 | 9154 |
60-70 | 40 | 65 | 2600 | 9.95 | 99 | 3960 |
70-80 | 60 | 75 | 4500 | 0.05 | 0.0025 | 0.15 |
80-90 | 35 | 85 | 2975 | 10.05 | 101 | 3515 |
90-100 | 16 | 95 | 1520 | 20.05 | 402 | 6432 |
100-110 | 09 | 105 | 945 | 30.05 | 903 | 8127 |
110-120 | 06 | 115 | 690 | 40.05 | 1604 | 9624 |
Σƒ=200 | Σƒm=14990 | Σƒd2=50699.15 |
From the above calculation we get that average IQ of all students is 74.95, and we get the standard deviation from IQ
If you are still wondering, what will we get from calculating? We can find the spread of the data by comparing the difference between the mean and standard deviation.
Let’s see how the widespread and densely populated data would look.
This can be a super guide for you to start and excel in your data science career.
ANCOVA is an extension of ANOVA (Analysis of Variance) that combines blocks of regression analysis and ANOVA. Which makes it Analysis of Covariance.
What if we learn topics in a desirable way!! What if we learn to write Python codes from gamers data !!
Start using NotebookLM today and embark on a smarter, more efficient learning journey!
List is one of the four data types in Python. Python allows us to create a heterogeneous collection of items inside a list.
NLP is a branch of AI that concerns with computers(AI) understanding natural languages.
Booleans are most important aspects of programming languages.
Booleans are most important aspects of programming languages.
Sentiment analysis can determine the polarity of sentiments from given sentences. We can classify them into certain ranges positive, neutral, negative
Strings is one of the important fundamental datatypes in python. Interactions of input and output console’s are conveyed using strings.
Read this article further to know where to use stemmers and lemmatization. Lemmatization maybe better than stemmer but is it worth your time.
This article will walk you through the different data types of numbers.
TF-IDF method belongs to domain of information retrieval,
Leave a Reply
You must be logged in to post a comment.