Definitions [1]
Define the mean.
The mean is the value that is derived by summing all the values and dividing it by the number of observations.
`bar"x" = "Sum of observations"/"No. of observations"`
Formulae [4]
-
For Individual or Ungrouped Data
\[\mathrm{Q}_i=\text{size of }i\left(\frac{n+1}{4}\right)^\text{th Observation.}\quad i=1,2,3\]
-
For Grouped/Continuous Data
\[\mathbf{Q}_i=l+\left(\frac{\frac{in}{4}-cf}{f}\right)\times h\quad i=1,2,3\]
Where
l = Lower limit of quartile class.
f = Frequency of the quartile class
cf = Cumulative frequency of the class preceding the quartile class.
n = Total of frequency.
h = Upper limit - lower limit of the quartile class.
Step - I : First find the value of quartile
\[\mathrm{Q}_1=\mathrm{size~of}\left(\frac{n}{4}\right)^{\text{th Observation}}\]
\[\mathrm{Q}_1=\mathrm{size~of}\left(\frac{3n}{4}\right)^{\text{th Observation}}\]
Step - II :
\[\mathbf{Q}_i=l+\left(\frac{\frac{in}{4}-cf}{f}\right)\times h\quad i=1,2,3\]
Where
l = Lower limit of quartile class.
f = Frequency of the quartile class.
cf = Cumulative frequency of the class preceding the quartile class.
n = Total of frequency.
h = Upper limit - lower limit of the quartile class.
1. For Individual or Discrete Data:
\[\mathrm{D}_j=j\left(\frac{n+1}{10}\right)^\text{th Observation}\mathrm{~where~}j=1,2...9\]
2. For Grouped (Continuous) Data:
\[\mathbf{D}_j=l+\left(\frac{\frac{jn}{10}-cf}{f}\right)\times h,\quad j=1,2...9\]
Where
D = Decile
l = Lower limit of decile class
f = Frequency of decile class
cf = Cumulative frequency of class preceding decile class
h = Upper limit of the class – lower limit of the decile class.
A. For Individual or Discrete Data
Formula:
\[\mathrm{P}_k=\mathrm{size~of}k\left(\frac{n+1}{100}\right)^\text{th Observation}\] k = 1, 2,... 99
Where:
- k = Percentile number (1 to 99)
- n = Total number of observations
B. For Grouped/Continuous Data
Formula:
\[\mathbf{P}_k=l+\left(\frac{\frac{kn}{100}-cf}{f}\right)\times h\] k = 1, 2,... 99
Where
P = Percentile
l = Lower limit of percentile class
f = Frequency of percentile class
cf = Cumulative frequency of class preceding percentile class
h = Upper limit of the class – lower limit of the percentile class.
