Name:
Per:
CALCULATING STANDARD DEVIATION and STANDARD ERROR OF THE MEAN
These papers will be turned in for grading. When they are returned, please tape them into your notebook.
The standard deviation is used to tell how far on average any data point is from the mean. This is
sometimes called the variance from the mean. The smaller the standard deviation, the closer the scores
are on average to the mean. When the standard deviation is large, the scores are more widely spread
out on average from the mean. Standard error of the mean measures the accuracy and validity of your
data. A lower standard of error is more valid than a high SE.
PRACTICE PROBLEM #1 Student Height
a. Find your height in centimeters and post it on the whiteboard. When everyone’s data has been
collected, calculate the mean and standard deviation.
b. Now, on the bell shaped curve/normal distribution below, put the mean height in the top box. Then
subtract the S from the mean and put it in box b. Subtract the S from the mean twice and put it into
box c, three times for box d. Then add the standard deviation to the mean and fill in box e, etc.
Calculate the percent of students’ whose height is within each standard deviation and add it to the
graph in the appropriate boxes.
c.
Now calculate the standard error of the mean for the height data.
d. Once you’ve calculated SEM, place error bars for standard deviations 1 and 2 on the graph above.
Because the Y axis does not have increments, you will have to estimate the position of the error bars.
PRACTICE PROBLEM #2
The data set below gives the numbers of home runs for the 10 batters who hit the most home runs during
the 2005 Major League Baseball regular season.
51, 48, 47, 46, 45, 43, 41, 40, 40, 39
Use one of the class computers and Microsoft Excel to calculate the standard deviation and SEM of the
class data.
a. Using MS Excel to calculate standard deviation:
Type the data in any column on the spreadsheet, going down from box to box.
In any empty box where you would like Standard Dev. to appear, type =stdev(
Select the data you are working with then type ) space enter
The standard deviation for that data should be automatically calculated in that box.
b. Calculate standard error by typing into an empty box =(C14/SQRT(24))enter
Change the numbers in gray to the appropriate values.
 The first number in gray represents the name of the spreadsheet box that now contains
the standard deviation.
 The second number in gray represents the number of scores being studied.
c.
Create a bar graph of the data using Excel by selecting the boxes that have your data, selecting
the “Insert” tab and choosing the type of graph you want.
d. Add error bars to your graph:
a. click anywhere on your graph
b. Click the Layout Tab and find Analysis group. You will see a selection for Error Bars.
c. Choose “Error Bars with Standard Error” which will add error bars to your graph.
We do not have a network printer in this classroom. Please print your batting scores
data, calculations and graph at home or in the library, staple it to this sheet and turn it
in tomorrow.
After this is graded and returned, please tape these sheets into your notebook.