# Baseline Calculations

Some views include baseline data as a basis for comparison. The baseline calculation method varies by the registered data source. The baseline data that is plotted in many views shows statistical deviations from "normal" performance for a given statistic. Metrics are considered to be "normal" based on the calculated baseline average. The Standard Deviation is used to gauge the statistical validity of the baseline values. Baseline values are included in charts to help you see places where performance values are changing rapidly.
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Some views include baseline data as a basis for comparison. The baseline calculation method varies by the registered data source. The baseline data
that is plotted in many views shows statistical deviations from "normal" performance for a given statistic. Metrics are considered to be "normal" based on the calculated baseline average. The Standard Deviation is used to gauge the statistical validity of the baseline values. Baseline values are included in charts to help you see places where performance values are changing rapidly.
Baseline data helps to characterize past performance for selected monitored parameters, assess present performance, and estimate future performance. For example, comparing current CPU utilization to a known baseline average level helps to determine whether current utilization is within a typical range. A monitored parameter that exceeds a baseline can indicate additional load on the server from a new application process, an increase in the number of users or sessions, or an increase in the amount of data being processed.
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Baseline Averages
Depending on the amount of polled data that is collected,
baseline averages
are calculated in two ways:
• Initially, averages are calculated for the same hour regardless of the day.
• After enough data is collected, averages are calculated for the same day of the week and the same hour.
Baseline averages help to characterize past performance for selected monitored metrics, and helps to assess present performance. Baseline averages and related standard deviations are continually calculated as each hour passes. The standard deviation provides a statistical indicator of how much variability exists in the population data that factored into the baseline average calculations.
In Data Aggregator, "normal" for a specified duration within a window of time is based on the calculated baseline average.
Baseline Average Calculations
When a limited amount of data is first collected, the baseline average is calculated for the same hour for every preceding day of the week. For example, after two days worth of history, a baseline average value for the 9:00 AM to 10:00 AM time period is calculated by averaging the hourly rollups for the same time periods for two consecutive days.
Eventually, when more data is available, a switchover in the calculation method occurs automatically and Data Aggregator establishes "normal" by averaging hourly samples across available preceding same days of the week. This method, then, considers the day of the week patterns in utilization. This method produces a better approximation of what is "normal", which can lead to a reduction in the number of missed violations and false positive events that are generated. In the same example as above, after three weeks of history, a baseline average is calculated by averaging the 9:00 AM to 10:00 AM hourly rollups for the three Mondays within the three-week period.
By default, this automatic switchover occurs when at least three same day of the week, same hour data samples are available for the past 12 weeks. Data Aggregator switches back to the every day, same hour calculation method automatically when the required number of data points is no longer available. These default settings are configurable. For more information, see Configure Data Retention Rates.
Baseline averages are calculated for event and report generation purposes.
Standard Deviation Calculations
The standard deviation is calculated from the baseline average for rollups, threshold events, and report generation purposes.
Rollups:
• For hourly rollups, the standard deviation is calculated for the polled values.
• For daily rollups, the standard deviation is calculated for hourly averages.
• For weekly rollups and beyond, the standard deviation is calculated for the daily averages.
Threshold Events:
• The standard deviation provides a statistical indicator of how much variability exists in the population data that factored into the baseline average calculations.
Reporting:
• For hourly reporting, the standard deviation is calculated for the polled values.
• For daily reporting, the standard deviation is calculated for hourly averages.
• For weekly reporting and beyond, the standard deviation is calculated for the daily averages.
The formula for calculating this standard deviation is:
`population deviation = Square root of (Sum ( X - population mean)/number of data points)`
• X
The data point value in the population
• Population
The set of potential values that includes observed cases and potentially observable cases
Example: Calculate the Same Hour Average and Population Standard Deviation for CPU Utilization
The following example shows how the "same hour" average (mean) and population standard deviation are calculated for CPU utilization on a specific device, when there are three points of data for 2:00 AM on Monday, Tuesday, and Wednesday.
1. Collect three points of data.
`Day:                               Monday       Tuesday      WednesdayMean (Average) CPU utilization:    76           65           10`
2. Calculate the population mean.
The formula for calculating the population mean is as follows:
`The population mean = sum of data point values in population/number of data points.`
The equation for this example is as follows:
`(76+65+10)/3The population mean= 50.33`
3. Calculate the difference of each data point from the mean.
The differences for this example are:
`25.67    14.67    -40.33`
4. Calculate the square of the difference for each data point.
The squares for this example are:
`658.78     215.11    1,626.778`
5. Calculate the sum of the squares:
The sum of the squares for this example is 2,500.67.
6. Calculate the sum of the squares, divided by the number of data points in the population.
The result for this example is 833.56.
7. Calculate the square root of the sum of squares of data point value from the population mean.
The square root for this example is 28.87.
The standard deviation for this example is 28.87.
The following table depicts the hourly averages (mean) of rate data by day, the average (mean) of hourly averages, and the population standard deviation of the hourly averages for the same hour:
 Time Monday Tuesday Wednesday ... Mean Standard Deviation 2:00 AM 76 65 10 ... 50.33 28.87 3:00 AM 87 18 32 ... 45.67 29.78 4:00 AM 10 56 40 ... 35.33 19.07 5:00 AM 60 45 19 ... 41.33 16.94 Hour... ... ... ... ... ... ...
Example: Calculate the Same Day of the Week Same Hour Average and Population Standard Deviation for CPU Utilization
The following example shows how the average (mean) and population standard deviation are calculated for CPU utilization on a specific device, when there are three points of data for three Mondays at 2:00 AM.
1. Collect three points of data.
`Monday of Week:                      1       2      3Mean (Averages) CPU utilization:    76       4      6`
2. Calculate the population mean.
The formula for calculating the population mean is as follows:
`The population mean = sum of data point values in population/number of data points.`
The equation for this example is as follows:
`(76+4+6)/3The population mean = 28.67.`
3. Calculate the difference of each data point from the mean.
The differences for this example are:
`47.33    -24.67    -22.67`
4. Calculate the square of the difference for each data point.
The squares for this example are:
`2,240.44    608.44    513.78`
5. Calculate the sum of the squares.
The sum of the squares for this example is 3,362.67.
6. Calculate the sum of the squares, divided by the number of data points in the population.
The result for this example is 1,120.89.
7. Calculate the square root of the sum of squares of the data point value from the population mean.
The square root for this example is 33.48.
The standard deviation for this example is 33.48.
The following table depicts the hourly averages (mean) of rate data by day, the average (mean) of hourly averages and the population standard deviation of the hourly averages for the same day of the week, same hour:
 Time Week 1 Week 2 Week 3 Monday Monday ... Monday ... Monday ... Mean Standard Deviation 2:00 AM 76 ... 4 ... 6 ... 28.67 33.48 3:00 AM 87 ... 71 ... 56 ... 71.33 12.66 4:00 AM 10 ... 27 ... 58 ... 31.67 19.87 5:00 AM 60 ... 3 ... 32 ... 31.67 23.27 Hour ... ... ... ... ... ... ... ...
Example: Deviation from Normal using the Same Day of the Week Same Hour Average and Population Standard Deviation for CPU Utilization
Assume that Data Aggregator is polling CPU utilization data at a 5-minute interval. You define an event rule to generate an event when CPU utilization is greater than one standard deviation above the mean for a single 5-minute poll interval.
In this example, event rule duration and window are both set to 5 minutes.
The formula for calculating when an event is raised is as follows:
`CPU utilization = mean value + 1(standard deviation value)`
Therefore, substituting mean and standard deviation values from the preceding same day of the week, same hour for Monday at 2:00 AM is as follows:
`CPU utilization = 28.67 + 1 (33.48)CPU utilization = 62.15`
As a result, if CPU utilization were to exceed 62.15 for a single 5-minute poll interval between 1:05 AM and 2:00 AM on Monday, an event would be raised. This event indicates that the CPU utilization deviated from normal for that timeframe.
Example: Examine CPU Utilization Events in a Trend Chart View
Assume that Data Aggregator is polling CPU utilization data at a 5-minute interval. In this example, you want to be alerted whenever CPU utilization on one of your business critical servers drops below the expected level. You define an event rule to generate an event when CPU utilization is one standard deviation below the mean for a single 5-minute poll interval.
For illustrative purposes only, assume that CPU utilization is 50 percent from Monday, 12:00 AM to Sunday, 12:00 AM. From Sunday, 12:00 AM to Monday, 12:00 AM, CPU utilization drops to 10 percent. You expect this drop in utilization. However, when Data Aggregator begins to calculate the baseline average, an event is raised when the CPU utilization drops to 10 percent. The event clears when the CPU utilization goes back up to 50 percent. The erroneous event is raised because, initially, when a limited amount of data is collected, the baseline average is calculated for the same hour for every day, not taking into account the difference in utilization across days of the week. Data Aggregator is expecting the CPU utilization to be 50 percent
always
.
After three weeks pass, three same days of the week, same hour data samples are available, and the baseline average calculation method changes. Data Aggregator establishes "normal" by averaging hourly samples across same days of the week. Data Aggregator is now expecting the CPU utilization to be 10 percent every Sunday at 12:00 AM to Monday at 12:00 AM. The erroneous event that was raised previously every Sunday at 12:00 AM is no longer raised.