Question

Calculate the standard deviation of the following set of measured values: 3.15,3.21,3.18,3.30,3.25,3.13,3.24,3.41,3.13,3.42,3.19

I calculated it but my answer was incorrect. Can you please do this problem and show the work step by step. I need to see where I went wrong. Thank you so much.

Answer 1

This is the formula for Standard Deviation:

To calculate the standard deviation of those numbers:

• 1. Work out the Mean (the simple average of the numbers)
• 2. Then for each number: subtract the Mean and square the result
• 3. Then work out the mean of those squared differences.
• 4. Take the square root of that and we are done!

3.15,3.21,3.18,3.30,3.25,3.13,3.24,3.41,3.13,3.42,3.19

Step 1. Work out the mean

The mean is = (3.15+3.21+3.18+3.30+3.25+3.13+3.24+3.41+3.13+3.42+3.19)/ 11

The mean is = 3.2372

so = 3.2372

Step 2. Then for each number: subtract the Mean and square the result

This is the part of the formula that says:

(3.15- 3.2372)² = 0.0076

(3.21- 3.2372)² = 0.00073

(3.18- 3.2372)² = 0.0032

(3.30- 3.2372)² = 0.0039

(3.25- 3.2372)² = 0.0001

(3.13- 3.2372)² = 0.0114

(3.24- 3.2372)² = 0.000007

(3.41- 3.2372)² = 0.0298

(3.13- 3.2372)² = 0.0114

(3.42- 3.2372)² = 0.0334

(3.19- 3.2372)² = 0.0022

Step 3. Then work out the mean of those squared differences.

To work out the mean, add up all the values then divide by how many.

i.e 0.103737 / 11= 0.009430

Step 4. Take the square root of that:

σ = 0.009430 = 0.09711  

is the standard deviation of the above set of measured values.