A discrete variation series is a sequence of values that is used to analyze and present data. Here are some basic formulas and concepts related to discrete variation series:
- Elements of the variation series:
- ( x_1, x_2, \ldots, x_n ) are elements of the discrete variational series.
- Frequency:
- ( f_i ) — frequency of occurrence of element ( x_i ) in the row.
- Relative frequency:
- ( p_i = \frac{f_i}{N} ), where ( N ) is the total number of elements in the row.
- Sum of frequencies:
- ( \sum_{i=1}^{n} f_i = N )
- Arithmetic mean:
- ( \bar{x} = \frac{\sum_{i=1}^{n} x_i}{N} )
- Dispersion:
- ( D = \frac{\sum_{i=1}^{n} (x_i – \bar{x})^2}{N} )
- Standard deviation:
- ( \sigma = \sqrt{D} )
- Fashion:
- The value ( x_i ) that has the highest frequency ( f_i ).
- Median:
- The value that divides a series into two equal parts. If ( N ) is even, the median is the average of the two central values.
- Cumulative frequency:
- ( F_i = \sum_{j=1}^{i} f_j ) — the sum of frequencies up to the element ( x_i ).