Standard deviation is a measurement for the variations from the mean, for a set of values. You usually use small sigma as a sign for standard deviation.

I was asked to create a solution which got measurements from BAC (HP) within a certain amount of time.

They wanted to display these values, the mean and recommended values for the thresholds (red/yellow) in a graph. I then thought I could create this by calculating the standard deviation.

These values were supposed to be measured within a “normal stability period”.

They wanted to calculate the recommended thresholds in which to set in BAC.

This is the formula for the standard deviation:

I used curl and BAC OpenApi to get the values from BAC.

I created a generic query, which got all the Monitors and transactions from BAC.

This query then created a «Select form», where you could choose which transaction you wanted to analyze.

When you choose the transaction, there is a query to the OpenApi with Curl and you get the timestamp and response for a given amount of time.

I parse this data and puts the values in different array’s.

I then get the sum of all the values in the response array.

I then get the amount of measurements in the response array, by using count($array_response) in php.

I then get the mean from this array by using the formula:

I then have to take each values in the array_respons minus the mean and exp in 2.

I then needed to take the square root of the sum of these values.

This value is the standard deviation.

sample php code:

(median_svar is the mean of the array)

foreach ( $array_response as $value ) {

$median_row=($value/1000)-$median_svar;

$expo+=($median_row*$median_row);

}

$median_endvalue=sqrt($expo/$antall_svar);

The standard deviation is $median_end_value.

Using Chebyshev’s inequality, I calculated the recommended thresholds for yellow and red in BAC.

I also took some considerations in the calculation of these thresholds by checking the

relation between the mean and the standard deviation.

Chebyshev’s inequality:

At least 50% of the values are within ?2 standard deviations from the mean.

At least 75% of the values are within 2 standard deviations from the mean.

At least 89% of the values are within 3 standard deviations from the mean.

At least 94% of the values are within 4 standard deviations from the mean.

At least 96% of the values are within 5 standard deviations from the mean.

At least 97% of the values are within 6 standard deviations from the mean.

At least 98% of the values are within 7 standard deviations from the mean.