There are two common ways you can statistically describe uncertainty in your measurements. Can we ever know the true energy values? No, but you can include additional information to indicate how closely the means are likely to reflect the true values. However, though you can say that the means of the data you collected at 20 and 0 degrees are different, you can't say for certain the true energy values are different. If you look back at the line graph above, we can now say that the mean impact energy at 20 degrees is indeed higher than the mean impact energy at 0 degrees. Once you have calculated the mean for the -195 values, then copy this formula into the cells C9, etc. In this case, the values in cells B4 through B8 are averaged (the mean calculated) and the result placed in cell B9. You use this function by typing =AVERAGE in the formula bar and then putting the range of cells containing the data you want the mean of within parentheses after the function name, like this: The mean was calculated for each temperature by using the AVERAGE function in Excel. Note that instead of creating a graph using all of the raw data, now only the mean value is plotted for impact energy. The above scatter plot can be transformed into a line graph showing the mean energy values: In this example, it would be a best guess at what the true energy level was for a given temperature. Without going into detail, the mean is a way of summarizing a group of data and stating a best guess at what the true value of the dependent variable value is for that independent variable level.
The mean, or average, of a group of values describes a middle point, or central tendency, about which data points vary. Can we say there is any difference in energy level at 0 and 20 degrees? One way to do this is to use the descriptive statistic, mean. These ranges in values represent the uncertainty in our measurement. In fact, there are a number of measurements at 0 degrees (shown in crosses) that are very close to measurements taken at 20 degrees (shown in light green triangles). On the other hand, at both 0 and 20 degrees, the values range quite a bit. At -195 degrees, the energy values (shown in blue diamonds) all hover around 0 joules. Notice the range of energy values recorded at each of the temperatures. The resulting data (and graph) might look like this:įor clarity, the data for each level of the independent variable (temperature) has been plotted on the scatter plot in a different color and symbol. Because there is not perfect precision in recording this absorbed energy, five different metal bars are tested at each temperature level.
In this case, the temperature of the metal is the independent variable being manipulated by the researcher and the amount of energy absorbed is the dependent variable being recorded. Let's take, for example, the impact energy absorbed by a metal at various temperatures. This distribution of data values is often represented by showing a single data point, representing the mean value of the data, and error bars to represent the overall distribution of the data. Though no one of these measurements are likely to be more precise than any other, this group of values, it is hoped, will cluster about the true value you are trying to measure. The knowledge that any individual measurement you make in a lab will lack perfect precision often leads a researcher to choose to take multiple measurements at some independent variable level. Untitled Document Using Error Bars in your Graph for Excel-2007
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