# Calculate the standard deviation for an exp. data set.

The standard deviation of a data set is a measure of the 'spread' of a distribution of data or other numerical values; it is a measure of variability within a particular data set. To calculate standard deviation of a sample, generally the variance of the sample is first calculated. The variance is the average squared deviation of each number from its mean, and is given by the following equation: where m is the mean and N is the number of values within the data set of interest. For example, for the data set: 1, 2, and 3, the mean is 2 and the variance is given by the following:

The standard deviation of a sample is simply the square root of the variance, and is probably the most commonly used measure of data 'spread.'

For this CLC exercise;

a) Calculate the standard deviation for the experimentally obtained values of Keq, DH, and the values calculated for DG, and DS. Then post the results of these individual experiments, not the mean values, to the CLC group, and calculate standard deviation for those same values, using the entire data set generated by your CLC group.

b) How do your values compare to the values of the entire data set generated by your CLC group?

c) How 'tight' is the spread of the data?

d) Compare the values of both your personal data set and those of the CLC groups data set with the following accepted values as reported by Pickering (Pickering 1987) shown in the table below:

Variable Value

DH/kJ mol-1 17.6 ± 7.2

DG/kJ mol-1 -5.77 ± 0.63

DS/J mol-1 K-1 77.0 ± 28

i) How do your value compare to these experimentally obtained values?

ii) What are some possible sources of error in your measurement?

iii) Where there any extreme outliers in the data set you analyzed that might affect the pooled values?

#### Solution Preview

I have given you a formatted response in the word document attached, but it's pasted here for you as well.

Work together and come up with the answers to the following problem. Prepare a single group document, and submit it to the instructor by the end of Week 8.

The standard deviation of a data set is a measure of the 'spread' of a distribution of data or other numerical values; it is a measure of variability within a particular data set. To calculate standard deviation of a sample, generally the variance of the sample is first calculated. The variance is the average squared deviation of each number from its mean, and is given by the following equation, where m is the mean and N is the number of values within the data set of interest.

I'll give a more detailed example with some completely made up numbers.

Terms to remember:

mean = average

devation from mean = subtract your number from the mean (doesn't matter if it's negative since you'll be multiplying it by itself, squaring)

So, let's say we have 4 numbers: 18.5, 27.3, 20.2, and 19.8 (thus, N=4)

The average (m) is (18.5+27.3+20.2+19.8)/4 = 21.45

(don't round off until the end)

The deviation of the first value from the mean is 18.5-21.45=2.95

The deviation of the second value from the mean is 27.3-21.45=5.85

The deviation of the third value from the mean is 20.2-21.45=1.25

The deviation of the fourth value from the mean ...

#### Solution Summary

The solution and a complete explanation are provided for how to determine standard deviation from experimental data. Experimental error from a known value is also calculated and explained.