Calculating Average and Standard Deviation Hardness Values
How do we compute average and standard deviation hardness values based on the given data?
Below are tabulated a number of Rockwell G hardness values that were measured on a single steel specimen:
49.8, 49.9, 47.0, 48.1, 50.4, 49.1, 47.7, 49.9, 48.4, 48.4, 48.7, 50.0
Answer:
The average hardness value is 49.37 and the standard deviation is 1.12.
To compute the average and standard deviation hardness values, we can use the following steps:
- Add up all the hardness values: 49.8 + 49.9 + 47.0 + 48.1 + 50.4 + 49.1 + 47.7 + 49.9 + 48.4 + 48.4 + 48.7 + 50.0 = 592.4.
- Divide the sum by the total number of values: 592.4 / 12 = 49.37 (rounded to two decimal places). This is the average hardness value.
- To calculate the standard deviation, subtract the average from each hardness value, square the differences, sum them up, divide by the total number of values, and take the square root. Applying this formula gives us a standard deviation of 1.12 (rounded to two decimal places).
Therefore, the average hardness value is 49.37 and the standard deviation is 1.12.