Standard deviation measures the spread of data distribution from the mean or average.The more spread out a data distribution is from the mean, the greater its standard deviation.

So, in the distributions shown below the green distribution ranges from 2 to 8 whereas the blue distribution ranges from 0 to 10. Therefore, the blue distribution has a greater standard deviation.

One way of visualizing the spread of data around a mean is with a bell curve. A skinnier bell curve (blue curve) demonstrates that there is a smaller standard deviation and most of the data is centered around the mean. A flatter bell curve (red curve) has a larger deviation and more of the data is spread out.

Standard Deviation can also be depicted on a graph usingError Bars.

This is indicated by a line T shaped line extending vertically from the top of a column on a graph as shown below:

A B C D E

These lines depict one standard deviation above and below the mean of the data (which is represented by the top of the blue column). As you can see column B has a very small standard deviation and its error bars don't extend much from the column. However, column E has a large standard deviation and its error bars extend far from the column.

(A) What does the error bars tell you about the data that was collected for column B? What about column E?

When comparing sets of data, they are consideredsignificantly differentif the standard deviation barsdo NOT overlap. This is the case when comparing column A and column D. Data isNOTsignificantly different if the error barsdo overlap. This is the case of Columns A and B, A and C, A and E, etc.

(B) Using the data presented in the chart below, is the data significantly different or not significantly different? How do you know? Be sure to answer in complete sentences.

(C) Using the data presented in the chart below, is the data significantly different or not significantly different? How do you know? Be sure to answer in complete sentences.

(D) When do you think collecting standard deviation would be helpful in understanding your data? Are there any situations in your major or future degree or life you think that this may be helpful?