Update pages/5_Descriptive Statistics.py

pages/5_Descriptive Statistics.py

@@ -316,7 +316,9 @@ 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)
 
@@ -338,4 +340,55 @@ st.latex(r'''
 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**
+
+--->to check the consistency of data co-efficient of variance is used'''
+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}}''')
+
+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)