[Standard Deviation Pt. I] [Statistical Analysis of Data]

Standard Deviation Part II

Standard deviation is a mathematical tool to help us assess how far the values are spread above and below the mean.

A high standard deviation shows that the data is widely spread (less reliable) and a low standard deviation shows that the data are clustered closely around the mean (more reliable).

Standard deviation can also be used to help decide whether the difference between two means is likely to be significant (Does it support the hypothesis?).

Example 1:

Hypothesis: The berries from the tree with yellow & green leaves will be smaller than the berries from a tree with all-green leaves.

The difference in mean berry mass between the 2 tree types is 28 mg. The standard deviations are 73 mg and 80 mg.

Because the standard deviations are much bigger than the difference between the means, this means the data do not support the hypothesis. Even though the difference between the means of the two sets of berries is 30 mg, the difference is not significant enough to support the hypothesis.

Example 2:

Hypothesis: Rats living on Vancouver Island are longer the rats found on the west coast of Canada.

a) Calculate the difference in mean length between Vancouver and West Coast Rats:_____ ? _____

b) Are the Vancouver Island rats longer or shorter than those from the mainland? ______ ? _______

c) Are the standard deviations for the 2 rat populations greater or smaller than the difference in the mean?___ ? ____

d) Is the hypothesis supported or not supported by the data?______ ? ______

Example 3:

Hypothesis: Gatorade hydrates cells better than water.

a) Calculate the difference in mean change in mass between the two solutions ______ ? ______

b) Which hydrated cells better, Gatorade or water? _______ ? ______

c) Are the standard deviations smaller or greater than the difference in mean % Change in Mass?________ ? _________

d) Was the hypothesis supported? ________ ? _________