Definitions [5]
Frequency Distribution Table: When the number of observations in an experiment is large then we can convert it into the tabular form which is called a Frequency Distribution Table.
Ungrouped Frequency Distribution Table: When the frequency of each class interval is not arranged or organized in any manner.
Grouped Frequency Distribution Table: The frequencies of the corresponding class intervals are organised or arranged in a particular manner, either ascending or descending.
Inclusive or discontinuous Frequency Distribution: A frequency distribution in which the upper limit of one class differs from the lower limit of the succeeding class is called an Inclusive or discontinuous Frequency Distribution.
Exclusive or continuous Frequency Distribution: A frequency distribution in which the upper limit of one class coincides from the lower limit of the succeeding class is called an exclusive or continuous Frequency Distribution.
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"`
The arithmetic mean (or, simply, mean) of a set of numbers is obtained by dividing the sum of the numbers in the set by the number of numbers.
\[\mathbf{Mean}=\frac{\left(x_1+x_2+x_3+\ldots+x_n\right)}{n}=\frac{\Sigma x_i}{n}\]
Median is the value of the middle-most observation(s). The median is a measure of central tendency which gives the value of the middle-most observation in the data.
The mode is the value of the observation that occurs most frequently; i.e., the observation with the maximum frequency is called the mode.
Formulae [3]
Direct Method:
\[\bar{x}=\frac{\sum f_ix_i}{\sum f_i}\]
where xi = class mark, fi = frequency
Short-cut (Assumed Mean) Method:
\[\bar{x} = A+\frac{\sum f_id_i}{\sum f_i}\]
where di = xi - A
A is the assumed mean
Step-deviation Method:
\[\bar{x}=a+h\frac{\sum f_iu_i}{\sum f_i}\]
where \[u_i=\frac{x_i-a}{h}\]
h is the class width / common factor
If the number of data points (n) is odd, the median is,
Median = `((n+1)/2)^(th)` term
If n is even, the median is the average of the values at positions
Median = Average of `(n/2)^(th)` and `(n/2+1)^(th)` values
