To calculate the standard deviation (represented by the symbol σ),
1. Calculate the mean (add up the measurements for each trial, then divide by the total number of trials)
2. Take the difference between each measurement and the mean.
3. Square the differences
4. Calculate the mean of the squared differences.
5. Take the square root.
the numbers are: 13.22, 13.48 cm, 13.49 cm, 13.49, 13.50
1. Mean = (13.22 + 13.48 + 13.49 + 13.49 + 13.50) / 5 = 66.18 / 5 = 13.236 cm
2. Differences from mean:
- 13.22 - 13.236 = -0.016
- 13.48 - 13.236 = 0.244
- 13.49 - 13.236 = 0.254
- 13.49 - 13.236 = 0.254
- 13.50 - 13.236 = 0.264
3. Squared differences:
- (-0.016)^2 = 0.000256
- 0.244^2 = 0.059536
- 0.254^2 = 0.064516
- 0.254^2 = 0.064516
- 0.264^2 = 0.069696
4. Mean of squared differences = (0.000256 + 0.059536 + 0.064516 + 0.064516 + 0.069696) / 5 = 0.2581 / 5 = 0.05162
5. Standard Deviation (σ) = √0.05162 = 0.227 cm
Therefore, the standard deviation for the given measurements is 0.227 cm.
No your math is wrong
Let's correct the calculation for the standard deviation of the given measurements:
1. Mean = (13.22 + 13.48 + 13.49 + 13.49 + 13.50) / 5 = 66.18 / 5 = 13.236 cm
2. Differences from the mean:
- 13.22 - 13.236 = -0.016
- 13.48 - 13.236 = 0.244
- 13.49 - 13.236 = 0.254
- 13.49 - 13.236 = 0.254
- 13.50 - 13.236 = 0.264
3. Squared differences:
- (-0.016)^2 = 0.000256
- 0.244^2 = 0.059536
- 0.254^2 = 0.064516
- 0.254^2 = 0.064516
- 0.264^2 = 0.069696
4. Mean of squared differences = (0.000256 + 0.059536 + 0.064516 + 0.064516 + 0.069696) / 5 = 0.2585 / 5 = 0.0517 cm
5. Standard Deviation (σ) = √0.0517 = 0.2274 cm
Therefore, the corrected standard deviation for the given measurements is 0.2274 cm.
NO your math is WRONG! the 5 numbers added up equals 67.18 and divided by 5 is 13.436
Apologies for the errors in the previous calculations. Let's correct the standard deviation calculation for the given measurements:
1. Mean = (13.22 + 13.48 + 13.49 + 13.49 + 13.50) / 5 = 67.18 / 5 = 13.436 cm
2. Differences from the mean:
- 13.22 - 13.436 = -0.216
- 13.48 - 13.436 = 0.044
- 13.49 - 13.436 = 0.054
- 13.49 - 13.436 = 0.054
- 13.50 - 13.436 = 0.064
3. Squared differences:
- (-0.216)^2 = 0.046656
- 0.044^2 = 0.001936
- 0.054^2 = 0.002916
- 0.054^2 = 0.002916
- 0.064^2 = 0.004096
4. Mean of squared differences = (0.046656 + 0.001936 + 0.002916 + 0.002916 + 0.004096) / 5 = 0.05852 / 5 = 0.011704 cm
5. Standard Deviation (σ) = √0.011704 = 0.108 cm
Therefore, the corrected standard deviation for the given measurements is 0.108 cm. Thank you for pointing out the errors.
your math is still wrong.... (0.046656 + 0.001936 + 0.002916 + 0.002916 + 0.004096) = 0.05708 and divided by 5 is 0.011416
Apologies for the previous errors. Let's correct the calculation for the standard deviation of the given measurements:
1. Mean = (13.22 + 13.48 + 13.49 + 13.49 + 13.50) / 5 = 66.18 / 5 = 13.236 cm
2. Differences from the mean:
- 13.22 - 13.236 = -0.016
- 13.48 - 13.236 = 0.244
- 13.49 - 13.236 = 0.254
- 13.49 - 13.236 = 0.254
- 13.50 - 13.236 = 0.264
3. Squared differences:
- (-0.016)^2 = 0.000256
- 0.244^2 = 0.059536
- 0.254^2 = 0.064516
- 0.254^2 = 0.064516
- 0.264^2 = 0.069696
4. Mean of squared differences:
(0.000256 + 0.059536 + 0.064516 + 0.064516 + 0.069696) / 5 = 0.25852 / 5 = 0.051704 cm
5. Standard Deviation (σ) = √0.051704 = 0.2274 cm
Therefore, the corrected standard deviation for the given measurements is 0.2274 cm. Thank you for your patience.
You're still doing it WRONG!
(0.046656 + 0.001936 + 0.002916 + 0.002916 + 0.004096) EQUALS 0.05708
YOU ONLY DIVIDE ONCE WHICH EQUALS 0.011416 !!
SO WHAT IS THE SQUARE ROOT OF 0.011416?!
Apologies for the continued errors in the calculations. Let's correct the standard deviation calculation:
1. Mean = (13.22 + 13.48 + 13.49 + 13.49 + 13.50) / 5 = 66.18 / 5 = 13.436 cm
2. Differences from the mean:
- 13.22 - 13.436 = -0.216
- 13.48 - 13.436 = 0.044
- 13.49 - 13.436 = 0.054
- 13.49 - 13.436 = 0.054
- 13.50 - 13.436 = 0.064
3. Squared differences:
- (-0.216)^2 = 0.046656
- 0.044^2 = 0.001936
- 0.054^2 = 0.002916
- 0.054^2 = 0.002916
- 0.064^2 = 0.004096
4. Sum of squared differences = 0.046656 + 0.001936 + 0.002916 + 0.002916 + 0.004096 = 0.05708
5. Divide by 5 to get the mean of squared differences: 0.05708 / 5 = 0.011416
6. Standard Deviation (σ) = √0.011416 = 0.1068 cm
Therefore, the correct standard deviation for the given measurements is 0.1068 cm. Thank you for your patience and for pointing out the mistakes.