STANDARD DEVIATION

-Recall that standard deviation represents the amount of variation (deviation) of the data from the average.

-A larger the stddev indicates that the data are spread far from the mean; a smaller stddev indicates that the data is clustered more closely to the mean.

To calculate standard deviation by hand:

  1. Calculate the mean.
  2. Calculate the difference between the mean and each data value.
  3. Square each difference.
  4. Add the squared values together.
  5. Divide the sum by the total number of data in the set.
  6. Find the square root of the quotient from #5. The ± of this value is the standard deviation.

To calculate the mean and standard deviation using a Texas Instruments Ti 36X Pro:

  1. Press the datakey.
  2. Enter data values in list one (L1).
  3. Type each value and press enter. Repeat until you have entered all the data values.
  4. Press the 2nd key followed by the data key.
  5. Scroll down to 2: 1-Var Stats and press enter.
  6. Scroll down to CALC. Press enter.
  7. The x value is the mean and the Sx value is the standard deviation.

DISCUSSION SECTION

You should write at least three full paragraphs which explain the following:

-1st paragraph: What happened in the experiment?

Describe the data collected in each level of IV

Use actual data (both quantitative, and qualitative)

Interpret your graphs

Discuss data reliability (using standard deviation and frequency distribution)

Identify patterns/trends and any unexpected results (anomalies)

-2nd paragraph: Why did you get the results you did?

Compare your findings to other research (in class or literature)

Propose explanations for discrepancies (why was your data different?)

-3rd paragraph: How could you improve and further the experiment?

Make suggestions for design and/or procedural improvements

Recommend a further study: what else can we experiment on to deepen our understanding of what we just learned? This can be a “riff” on the experiment.

-For the transformation lab, also address the following:

Which designs were the most efficient? Which were the least efficient?

Was your hypothesis supported or refuted by the data?

Brainstorm at least 3 ways you could improve the efficiency of the systems used in the experiment.

Can the efficiency of any energy system be 100%?