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Standard Deviation
Standard Deviation is square root of variance. It is a measure of the extent to which data varies from the mean.
Standard Deviation (for above data) = √4 = 2
Why did mathematicians chose square and then square root to find deviation, why not simply take difference of values?
One reason is the sum of differences becomes 0 according to definition of mean. Sum of absolute differences could be an option, but with absolute differences it was difficult to prove many nice theorems.
Some Interesting Facts:
1) Value of standard deviation is 0 if all entries in input are same.
2) If we add (or subtract) a number say 7 to all values in input set, mean is increased (or decreased) by 7, but standard deviation doesn’t change.
3) If we multiply all values in input set by a number 7, both mean and standard deviation are multiplied by 7. But if we multiply all input values with a negative number say -7, mean is multiplied by -7, but standard deviation is multiplied by 7.
The document Standard Deviation | Engineering Mathematics - Civil Engineering (CE) is a part of the Civil Engineering (CE) Course Engineering Mathematics.
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FAQs on Standard Deviation - Engineering Mathematics - Civil Engineering (CE)
| 1. What is standard deviation in computer science engineering (CSE)? |  |
Ans. Standard deviation in computer science engineering is a statistical measure that quantifies the amount of variation or dispersion in a set of data. It is used to understand how spread out the values are from the mean or average value. In CSE, standard deviation is commonly used to analyze and compare performance metrics, such as execution time or memory usage, in algorithms or programs.
| 2. How is standard deviation calculated in computer science engineering (CSE)? | |
Ans. In computer science engineering, the standard deviation is calculated by following these steps:
1. Calculate the mean (average) of the data points.
2. Subtract the mean from each data point and square the result.
3. Calculate the mean of the squared differences.
4. Take the square root of the mean squared difference to obtain the standard deviation.
| 3. What is the significance of standard deviation in computer science engineering (CSE)? | |
Ans. Standard deviation is of great significance in computer science engineering as it provides valuable insights into the variability or dispersion of data. It helps in understanding the reliability and consistency of measurements, performance metrics, or experimental results. By comparing standard deviations, CSE professionals can determine which algorithms, models, or systems have more consistent or stable performance, aiding in decision-making and optimization.
| 4. How is standard deviation used in analyzing data in computer science engineering (CSE)? | |
Ans. In computer science engineering, standard deviation is widely used to analyze data in various ways:
- It helps in identifying outliers or extreme values that deviate significantly from the mean, which may indicate errors or anomalies in the data.
- It enables the comparison of different sets of data by quantifying their variability, allowing CSE professionals to determine which set performs better or has more consistent results.
- It aids in making predictions or estimating confidence intervals, where standard deviation is used in conjunction with the mean to understand the expected range of values.
- It assists in assessing the performance and stability of algorithms or systems by analyzing the standard deviation of relevant metrics, such as response time or throughput.
| 5. Can standard deviation be negative in computer science engineering (CSE)? | |
Ans. No, standard deviation cannot be negative in computer science engineering or any other field of study. Standard deviation is always a non-negative value as it represents the square root of the mean squared difference from the mean. It measures the dispersion or spread of data, and therefore, it cannot have a negative value. If a calculated standard deviation appears to be negative, it indicates an error in the calculation or a mistake in the data being analyzed.
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