14. Estimate standard deviation for the following frequency distribution
[6]
Classes 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-99-1010-11 11-12 12-13 13-14
Frequencies 1 3 6 8 11 13 13 14 10 12 8 5 2
Answers
Step-by-step explanation:
The average depth of this river, x-bar, is found to be 4’.
Step 5: The sample variance can now be calculated:
Step 6: To find the sample standard deviation, calculate the square root of the variance:

Why is Standard Deviation Important?
Standard deviation is important because it measures the dispersion of data – or, in practical terms, volatility. It indicates how far from the average the data spreads. This helps you determine the limitations and risks inherent in decisions based on that data.
Real-life example: When considering investing in a stock, you can use standard deviation to determine risk. A stock with an average price of $50 and a standard deviation of $10 can be assumed to close 95% of the time (two standard deviations) between $30 ($50-$10-$10) and $70 ($50+$10+$10). It’s safe to assume that 5% of the time, it will plummet or soar outside of this range. If you were to compare this to a stock that has an average price of $50 but a standard deviation of $1, then it can be assumed with 95% certainty that the stock will close between $48 and $52. The second stock is less risky, more stable. The higher the standard deviation in relation to the mean, the higher the risk. Blue-chip stocks, for example, would have a fairly low standard deviation in relation to the mean.
Standard deviation has many practical applications, but you must first understand what it’s telling you about the data. Additionally, standard deviation is essential to understanding the concept and parameters around the Six Sigma methodology.