pages/5_Descriptive Statistics.py

import streamlit as st
st.title(":blue[DESCRIPTIVE STATISTICS]")
st.caption("***Elevate Your Insights: The Allure of Descriptive Statistics***")

st.image("https://cdn-uploads.huggingface.co/production/uploads/66bde9bf3c885d04498227a0/U57NME2YT_De7TsnyFPht.png",width=400)

multi = '''Descriptive Statistics is a branch of statistics which summarizes or describes the entire collected data. 
It focuses on presenting data in a meaningful way through measures and visualizations.
Descriptive statistics are commonly used in many fields including business, economics to summarize large amounts of data and provide a clear and concise understanding of its key characteristics
'''
st.markdown(multi)
st.markdown('''
    Descriptive statistics are divided into 3 types based on measures:
    
    :violet[1. Measures of Central Tendency]
    
    :violet[2. Measures of Variability (Dispersion)]
    
    :violet[3. Distribution] ''')

st.markdown(multi)

st.image("https://cdn-uploads.huggingface.co/production/uploads/66bde9bf3c885d04498227a0/3yOxh1hYH8zxksyrYo5R7.png")

st.header("1.Measures of Central Tendency",divider="red")
st.markdown('''It is used for measuring central or average value of the data.
This measure help to summarize a large data set by providing a single value that represents the "middle" or "central" point of the data distribution''')
multi='''There are mainly 3 types of Measures of central tendency:'''
st.markdown(multi)
multi=''':red[1. Mean]'''
st.markdown(multi)
multi=''':red[2. Median]'''
st.markdown(multi)
multi=''':red[3. Mode]'''
st.markdown(multi)

st.image("https://cdn-uploads.huggingface.co/production/uploads/66bde9bf3c885d04498227a0/uFpmO9i5sXkOK4gwl3By-.png",width=400)

st.subheader("1.Mean",divider="green")
multi = '''Mean is one of the best central tendency measure used to find the central value.
It uses all the observations of the data so that we can get accurate central data point.
Mean is calculated by summing all the data points and dividing by the number of data points.'''
st.markdown(multi)

st.latex(r'''
\text{Mean} = \frac{\sum_{i=1}^{n} x_i}{n}
''')

multi = '''
    There are 3 types of :
    
    :violet[1. Arithemetic mean]
    
    :violet[2. Geometric mean]
    
    :violet[3. Harmonic mean]'''
st.markdown(multi)
st.image("https://cdn-uploads.huggingface.co/production/uploads/66bde9bf3c885d04498227a0/UZDbaPifn2kfsYA5NlSNw.png",width=300)

st.subheader("a. Arithemetic Mean",divider="red")
multi = '''Arithmetic mean is sum of all the observations divided by the total number of observations.The data follows the arithmetic sequence'''
st.markdown(multi)
st.latex(r"\text{Arithmetic Mean} = \frac{\sum_{i=1}^{n} x_i}{n}")
multi = '''--->xi represents each data point

--->n is the total number of data points.'''
st.markdown(multi)

st.subheader("b. Geometric Mean",divider="red")
multi = '''Geometric mean of a series containing n observations is the nth root of the product of the observations.The data follows geometric sequence'''
st.markdown(multi)
st.latex(r"\text{Geometric Mean} = \left( \prod_{i=1}^{n} x_i \right)^{\frac{1}{n}}")
multi = '''--->xi represents each data point.

--->n is the total number of data points.

--->∏ denotes the product of all data points.'''
st.markdown(multi)

st.subheader("c. Harmonic Mean",divider="red")
multi = '''Harmonic mean is the reciprocal of the arithmetic mean.The data follows the harmonic sequence it means ratio'''
st.markdown(multi)
st.latex(r"\text{Harmonic Mean} = \frac{n}{\sum_{i=1}^{n} \frac{1}{x_i}}")
multi = '''--->xi represents each data point.

--->n is the total number of data points.

---> harmonic mean is particularly used for rates or ratios.'''
st.markdown(multi)

st.markdown('''Relation between above 3 types of mean is :
    ''')
st.latex(r"\text{Harmonic Mean} \leq \text{Geometric Mean} \leq \text{Arithmetic Mean}")
st.markdown('''If the every observation of collected data is same then mean is :
    ''')
st.latex(r"\text{Harmonic Mean} = \text{Geometric Mean} = \text{Arithmetic Mean}")
multi = '''Collected data has 2 types of mean :

population mean("**parameter**")
    
sample mean("**statistics**")
    '''
st.markdown(multi)
st.image("https://cdn-uploads.huggingface.co/production/uploads/66bde9bf3c885d04498227a0/fNxt5Geo3GZp5kZP0pHiV.png")
st.subheader("Population Mean",divider="violet")
st.markdown('''measure of population mean is probably known as parameter''')

st.latex(r"\text{Population Arithmetic Mean} (\mu) = \frac{1}{N} \sum_{i=1}^{N} x_i")

st.latex(r"\text{Population Geometric Mean} = \left( \prod_{i=1}^{N} x_i \right)^{\frac{1}{N}}")

st.latex(r"\text{Population Harmonic Mean} = \frac{N}{\sum_{i=1}^{N} \frac{1}{x_i}}")

st.subheader("Sample Mean",divider="violet")
st.markdown('''measure of sample mean is probably known as statistics''')

st.latex(r"\text{Sample Arithmetic Mean} (\bar{x}) = \frac{1}{n} \sum_{i=1}^{n} x_i")

st.latex(r"\text{Sample Geometric Mean} = \left( \prod_{i=1}^{n} x_i \right)^{\frac{1}{n}}")

st.latex(r"\text{Sample Harmonic Mean} = \frac{n}{\sum_{i=1}^{n} \frac{1}{x_i}}")

multi = '''--->N represents the total number of observations in the population - size of population data

--->n represents the total number of observations in the sample - subset of population data

--->xi represents each individual observation.'''
st.markdown(multi)

st.subheader("2.Median",divider="green")
multi = '''Median is one of the central tendency measure used to find the central value.
Median gives the precise central value of the data.
It uses only central values so we may not get accurate central point of the data.It is used mostly in ordered data.'''
st.markdown(multi)

multi=''':red[Odd number of observations]'''
st.markdown(multi)

st.latex(r"\text{Median} = x_{\left(\frac{n+1}{2}\right)}")

multi=''':red[Even number of observations]'''
st.markdown(multi)

st.latex(r"\text{Median} = \frac{x_{\left(\frac{n}{2}\right)} + x_{\left(\frac{n}{2} + 1\right)}}{2}")

st.subheader("3.Mode",divider="green")
multi = '''Mode is one of the central tendency value used to find the central data.
Mode gives the datapoint or value which is frequently occuring.It is mostly used in categorical data.

Types of Mode:
There are 5 types of mode. They are No mode, Unimode, Bimode, Trimode, and Multimode

:violet[No mode] - set of data which has no frequently ocuuring value then it contains no mode

:violet[Unimodal Mode] - set of data with one mode (frequently repeated values are 1) is known as a unimode.

:violet[Bimodal Mode] - set of data with two modes (frequently repeated values are 2) is known as a bimode

:violet[Trimodal Mode] - set of data with three modes(frequently repeated values are 3) is known as a Trimode

:violet[Multimodal Mode] - set of data with more than three modes(frequently repeated values are more than 3) is known as a multimode.'''
st.markdown(multi)

st.subheader("Outliers",divider="red")
multi = '''Outliers are data points that differ significantly from the majority of the data in a dataset.
Identifying and managing outliers is crucial for accurate data analysis as they can lead to misleading conclusions about central tendency and variability.'''
st.markdown(multi)

st.image("https://cdn-uploads.huggingface.co/production/uploads/66bde9bf3c885d04498227a0/mwVV5w-qU0LjiBiVnr-H3.png")

multi = '''Central tendency value can be corrupted by the outliers.If the dataset is having outlier then mean is pulled out by the outlier.

--->If the outliers are in dataset we have to use median as it is not effected by the outlier.If the outliers are more than 50% then only median will be effected -in this case the data is separated and statistical measures are calculated
'''
st.markdown(multi)

st.header("2.Measures of Dispersion(Variability)",divider="red")
multi = '''Measures of dispersion tells about how the collected data is dispersed or spread around the central value'''
st.image("https://cdn-uploads.huggingface.co/production/uploads/66bde9bf3c885d04498227a0/20BD0t7MzQ9dmV3FKmjUK.png",width = 300)

multi = '''Measures of dispersion is divided into 2 categories:

:blue[1.Absolute Measure]:If group of data spreads have same unit then absolute measure is used as it has same unit

:blue[2.Relative Measure]:If the group of data spreads have different units then relative measure is used as it is free from unit'''
st.markdown(multi)
st.image("https://cdn-uploads.huggingface.co/production/uploads/66bde9bf3c885d04498227a0/oJgs2OuROEi-w-xFLY6es.jpeg",width=300)

st.subheader("1.Absolute Measure",divider="blue")
multi='''There are 4 types of absolute measures:

:red[a. Range]

:red[b. Quantile deviation]

:red[c. Variance]

:red[d. Standard deviataion]'''
st.markdown(multi)

st.subheader("2.Relative Measure",divider="blue")
multi='''There are 4 types of relative measures:

:red[1. Co-efficient of Range]

:red[2. Co-efficient of Quartile Deviation]

:red[3. Co-efficient of Variation]

:red[4. Co-efficient of Standard Deviation]'''
st.markdown(multi)

st.image("https://cdn-uploads.huggingface.co/production/uploads/66bde9bf3c885d04498227a0/WbyJIpIHhQQwwwVSLzQ77.png",width = 300)

st.subheader("Range",divider="violet")
multi = '''Range is a measure of dispersion which gives the difference between maximum value and minimum value in the data spread.
It depends on unit as it is absolute range.

**Range = maximum - minimum**
'''
st.markdown(multi)

st.subheader("Co-efficient of range",divider="violet")
st.image('https://cdn-uploads.huggingface.co/production/uploads/66c760d3f1a4cc6587be7790/n-dJg048bp3IADdAYCH_K.png',width=300)

st.subheader("Quartile Deviation",divider="violet")
multi = '''Quartile deviation is inter-quartile range divided by two .
Inter-quartile range is difference between upper quartile and lower quartile in the distribution

Interquartile Range = Upper Quartile (Q3)–Lower Quartile(Q1)
It is known as Semi-Inter-Quartile Range i.e. half of the difference between the upper quartile and lower quartile'''
st.markdown(multi)

st.latex(r'''
\text{Quartile Deviation} = \frac{Q_3 - Q_1}{2}
''')

st.write("Where:")
st.latex(r'''
Q_3 \text{ is the third quartile (75th percentile)}
''')
st.latex(r'''
Q_1 \text{ is the first quartile (25th percentile)}
''')
st.subheader("Quartile Deviation",divider="violet")
multi = '''Quartile deviation is inter-quartile range divided by two .
Inter-quartile range is difference between upper quartile and lower quartile in the distribution.
IQR is to know the central 50% tendency value

Interquartile Range = Upper Quartile (Q3)–Lower Quartile(Q1)
It is known as Semi-Inter-Quartile Range i.e. half of the difference between the upper quartile and lower quartile'''
st.markdown(multi)

st.latex(r'''
\text{Quartile Deviation} = \frac{Q_3 - Q_1}{2}
''')

st.write("Where:")
st.latex(r'''
Q_3 \text{ is the third quartile (75th percentile)}
''')
st.latex(r'''
Q_1 \text{ is the first quartile (25th percentile)}
''')

multi = '''Quartile deviation only gives central 50% values that are close to median or not (it basically gives the behaviour of central data).

--->**More the spread then the deviation is high**
--->**spread is directly proportional to deviation**

Quartile deviation has some basic terms:

:red[Quantile]:To summarize the central tendency or dispersion - when quantiles(values) are dividing the data into equal parts then the part of dividing into equal parts are quantiles which are of 3 types

There are 3 types of quantile which divide the data:

:violet[1.Quartile]: divides the data into 4 equal parts 

:violet[2.Percentile]: when the data is going to divide into 100 equal parts that particular quantile is known as percentile

:violet[3.Decile]:when the data is going to divide into 10 equal parts that particular quantile is known as decile 
'''
st.markdown(multi)

st.subheader("Percentile Formula")
st.latex(r'''
L_p = \frac{p(n + 1)}{100}
''')
st.write("Where:")
st.latex(r'''
L_p \text{ is the } n \text{-th percentile,}
''')
st.latex(r'''
n \text{ is the number of observations,}
''')

st.subheader("Decile Formula")
st.latex(r'''
D_p = \frac{p(N + 1)}{10}
''')
st.write("Where:")
st.latex(r'''
D_p \text{ is the } p \text{-th decile,}
''')
st.latex(r'''
n \text{ is the number of observations,}
''')

st.subheader("Co-efficient of Quartile Deviation",divider="violet")
st.latex(r'''
\text{Coefficient of Quartile Deviation} = (\frac{Q_3 - Q_1}{Q_3 + Q_1})*100''')

st.subheader("Variance",divider="violet")
multi = '''Variance is used for measuring the dispersion or spread.Average of spread or dispersion is known as variance.
-->to check the consistency of data co-efficient of variance is used'''
st.markdown(multi)
st.latex(r'''
\sigma^2 = \frac{\sum (X_i - \mu)^2}{N}''')
multi = '''There are two types of variance:

:red[population variance]

:red[sample variance]'''
st.markdown(multi)

st.subheader("Population Variance")
st.latex(r'''
\sigma^2 = \frac{\sum_{i=1}^{N} (X_i - \mu)^2}{N}''')

st.subheader("Sample Variance")
st.latex(r'''
s^2 = \frac{\sum_{i=1}^{n} (X_i - \bar{X})^2}{n - 1}
''')

st.subheader("Co-efficient of variance",divider="violet")

st.subheader("Coefficient of Variance (Population)")
st.latex(r'''
\text{CV} = \left( \frac{\sigma}{\mu} \right) \times 100''')

st.subheader("Coefficient of Variance (Sample)")
st.latex(r'''
\text{CV} = \left( \frac{s}{\bar{X}} \right) \times 100''')


st.subheader("Standard Deviation",divider="violet")
multi = '''Variance can't be easily interpreted because we are doubling the deviation i.e.,variance is also doubled to overcaome this standard deviation is used.

--->**More the spread it means more the standard deviation**

--->**spread is directly proportional to the standard deviation**'''
st.markdown(multi)
st.latex(r'''
\sigma = \sqrt{\frac{\sum (X_i - \mu)^2}{N}}''')

multi = '''Outliers are detected by standard deviation.

If the points are away from 3 standard deviation they are considered as outliers.

3STD is used as treshold to check outliers'''
st.markdown(multi)

st.subheader("Co-efficient of Standard deviation",divider="violet")
st.latex(r'''
\text{Coefficient of Standard Deviation} = \frac{\sigma}{\mu}''')

multi = '''As the sample data is subset of population data there is a error known as sampling error ---> to overcome this error degree of freedom is used.

When the outliers are in the data the measure of dispersion is known as **MAD-Median Absolute Deviation**'''
st.markdown(multi)

st.subheader("Population standard deviation")
st.latex(r'''
\sigma = \sqrt{\frac{\sum (X_i - \mu)^2}{N}}''')

st.subheader("Sample standard deviation")
st.latex(r'''
s = \sqrt{\frac{\sum (X_i - \bar{X})^2}{n - 1}}''')

st.latex(r'''
\text{Population Coefficient of Standard Deviation} = \frac{\sigma}{\mu}''')

st.latex(r'''
\text{Sample Coefficient of Standard Deviation} = \frac{s}{\bar{X}}''')

multi = '''--->σ is the population standard deviation

--->s is the sample standard deviation

--->Xi represents each data point

--->μ is the population mean

--->Xˉ is the sample mean

--->N is the total number of data points in the population

--->n is the number of data points in the sample.'''
st.markdown(multi)

st.subheader("MAD(Median Absolute Deviation)",divider="blue")
multi = '''When the outliers are in the data the measure of dispersion is known as **MAD-Median Absolute Deviation**

--->It is a measure of variability of a dataset'''
st.markdown(multi)

st.latex(r'''
\text{MAD} = \text{median}(|X_i - \text{median}(X)|)''')

st.header("3.Measures of Distribution",divider="red")
multi = '''It tells about the shape of data and how the data looks and to know the pattern of the data.

To know whether the data is frequently occuring'''
st.markdown(multi)