The formula to calculate the change in index (ΔI) is:
\[ \Delta I = \frac{I_f - I_i}{I_i} \]
Where:
Change in index refers to the relative change in a specific index value over a period of time. This can be applied to various fields such as finance, economics, and science. For instance, in finance, it can refer to the change in a stock market index, while in science, it might refer to changes in an index measuring a particular property or phenomenon. Understanding the change in index helps in analyzing trends, making predictions, and making informed decisions based on the observed data.
Definition: Calculate the Reliable Change Index (RCI) to determine the significance of change in a measurement.
Formula: \( RCI = \frac{X_2 - X_1}{S \times \sqrt{2(1 - r)}} \)
Example: \( RCI = \frac{85 - 70}{10 \times \sqrt{2(1 - 0.8)}} \)
Definition: Calculate the change in value between two points.
Formula: \( \Delta V = V_2 - V_1 \)
Example: \( \Delta V = 150 - 100 \)
Definition: Calculate an index number to compare relative changes over time.
Formula: \( I = \frac{P_t}{P_0} \times 100 \)
Example: \( I = \frac{120}{100} \times 100 \)
Definition: Calculate the rate of change indicator for a given data set.
Formula: \( ROC = \frac{P_t - P_{t-n}}{P_{t-n}} \times 100 \)
Example: \( ROC = \frac{130 - 100}{100} \times 100 \)
