Calculate weighted average

To calculate the weighted average, you need to follow these steps:

Assign a weight to each value in the dataset based on its importance or relevance. The weights can be expressed as percentages, decimals, or fractions.

Multiply each value in the dataset by its corresponding weight.

Add up the weighted values.

Add up the weights.

Divide the sum of the weighted values by the sum of the weights.

Here's an example to illustrate the process:

Suppose you have the following dataset of test scores and their corresponding weights:

Text Score                                                                    Weighted

90                                                                                   0.3

80                                                                                   0.2

95                                                                                   0.5

To calculate the weighted average, you would multiply each test score by its corresponding weight, add up the weighted scores, and then divide by the sum of the weights:

(90 x 0.3) + (80 x 0.2) + (95 x 0.5) = 27 + 16 + 47.5 = 90.5

0.3 + 0.2 + 0.5 = 1

Therefore, the weighted average test score is 90.5.

Note that the weight assigned to each value must add up to 1 or 100% for the calculation to be correct. Also, keep in mind that the weighted average is influenced more by the values with higher weights.

Weighted moving average

Weighted moving average (WMA) is a statistical method of calculating an average of a time series dataset that places more weight on recent observations and less weight on older observations. It is similar to a simple moving average (SMA), but instead of assigning equal weights to each observation, WMA assigns different weights to each observation based on its age.

To Calculate the WMA, you need to follow these steps:

Assign weights to each value in the dataset, with the most recent values assigned the highest weights and the oldest values assigned the lowest weights.

Multiply each value in the dataset by its corresponding weight.

Add up the weighted values.

Add up the weights.

Divide the sum of the weighted values by the sum of the weights.

The formula for calculating WMA can be expressed as:

WMA = (w1x1 + w2x2 + ... + wnxn) / (w1 + w2 + ... + wn)

where:

x1, x2, ..., xn are the values in the dataset

w1, w2, ..., wn are the corresponding weights for each value

The weights can be calculated using a formula or a pre-determined set of values. One common method is to use an exponential smoothing factor to calculate the weights, where the weights decrease exponentially as the observations get older.

WMA is useful in situations where recent observations are more important than older observations in predicting future trends. It is commonly used in finance and economics for forecasting stock prices and other financial indicators.

Note that WMA requires a minimum number of data points to be effective, and the number of data points used to calculate the WMA is called the "window size". A larger window size will result in a smoother WMA, but may also introduce more lag in the forecast.

Simple moving average

Simple moving average (SMA) is a statistical method of calculating an average of a time series dataset. It is a commonly used method for smoothing out short-term fluctuations and identifying trends in data over a specific period of time.

To calculate the SMA, you need to follow these steps:

Choose a window size, which is the number of data points used to calculate the moving average. For example, if you are looking at daily stock prices over a period of 30 days, you could choose a window size of 10, which means you would calculate the moving average of the past 10 days.

Calculate the average of the first window of data points, then move the window by one data point and recalculate the average. Repeat this process until you have calculated the average for all windows of data points.

Plot the moving average values on a graph to identify trends and smooth out short-term fluctuations.

The formula for calculating SMA can be expressed as:

SMA = (x1 + x2 + ... + xn) / n

where:

x1, x2, ..., xn are the values in the dataset

n is the window size

For example, suppose you have the following dataset of daily stock prices over the past 10 days:

Day                                                     Stock Price

1                                                     100

2                                                     105

3                                                     110

4                                                     115

5                                                     120

6                                                     125

7                                                     120

8                                                     115

9                                                     110

10                                                     105

To calculate the SMA using a window size of 3, you would calculate the average for each 

window of 3 data points:

Day                 Stock Price                                                       SMA (window size 3)

1                 100

2                 105

3                 110                                                                               105

4                 115                                                                               110

5                 120                                                                               115

6                 125                                                                               120

7                 120                                                                               121.67

8                 115                                                                               120

9                 110                                                                               115

10                 105                                                                               110

The SMA values can then be plotted on a graph to identify trends and patterns in the data. In this example, the SMA indicates an overall downward trend in the stock price over the past 10 days.

Exponential moving average

Exponential moving average (EMA) is a statistical method of calculating an average of a time series dataset that gives more weight to recent observations and less weight to older observations. It is similar to a simple moving average (SMA), but instead of assigning equal weights to each observation, EMA assigns exponentially decreasing weights to each observation based on its age.

To calculate the EMA, you need to follow these steps:

Choose a smoothing factor, which is a value between 0 and 1 that determines the weight given to each observation. A higher smoothing factor gives more weight to recent observations, while a lower smoothing factor gives more weight to older observations.

Calculate the EMA for the first observation in the dataset by setting it as the initial value for the EMA.

Calculate the EMA for the next observation by multiplying the current observation by the smoothing factor, subtracting it from the previous EMA value multiplied by 1 minus the smoothing factor, and adding the result to the previous EMA value.

Repeat step 3 for all subsequent observations in the dataset.

The formula for calculating EMA can be expressed as:

EMA = (Price(t) x Smoothing Factor) + (EMA(y) x (1 - Smoothing Factor))

where:

Price(t) is the price of the asset at time t

EMA(y) is the EMA for the previous period (y)

Smoothing Factor is a value between 0 and 1 that determines the weight given to each observation.

For example, suppose you have the following dataset of daily stock prices over the past 10 

days:

Day                                                   Stock Price

1                                                 100

2                                                 105

3                                                 110

4                                                 115

5                                                 120

6                                                 125

7                                                 120

8                                                 115

9                                                 110

10                                                 105

To calculate the EMA with a smoothing factor of 0.2, you would start with the SMA of the first observation, which is 100. Then, for the second observation, you would calculate the EMA using the formula:

EMA(2) = (105 x 0.2) + (100 x 0.8) = 101

For the third observation, you would calculate the EMA using the formula:

EMA(3) = (110 x 0.2) + (101 x 0.8) = 101.8

Repeat this process for all subsequent observations to calculate the EMA for each day. The EMA values can then be plotted on a graph to identify trends and patterns in the data.