Standard Deviation and Standard Error Worksheet

Standard Deviation and Standard Error Worksheet
You will want to complete this worksheet before you do the inquiry lab, “Why Don’t Whales Have Legs?”. It will help
you to write a procedure that has enough data to analyze … hint: multiple trials.
Part 1: Watch the BozemanScience tutorial on Standard Deviation at http://www.bozemanscience.com/standarddeviation
Part 2: Watch the BozemanScience tutorial on Standard Error at http://www.bozemanscience.com/standard-error
Part 3: Complete the examples below.
The formula for standard deviation is:
Symbol Key
∑ = ‘sum of’
xi = the data point
n = size of sample
Lets start with a hypothetical data set. Below is a chart of the wingspan of 5 Painted Lady butterflies. They were all fed
the same food as larvae and are the same age.
Step 1: Calculate the mean wingspan and record the mean in each box in the column marked ‘mean’. To calculate the
mean add all of the wingspan measurements together and divide by 5.
Step 2: Subtract the wingspan of butterfly #1 from the mean. Record this number in the next column.
Step 3: Repeat step 2 for each butterfly.
Step 4: Square the calculation of the difference and record it in the next column. Repeat for each butterfly.
Step 5: Add all of the squares of the differences together.
Step 6: Total the number of samples and subtract 1
Step 7: Plug the numbers into the formula above for standard deviation and get the square root. This is your standard
deviation!
Butterfly # Wingspan Mean Difference between data point and mean
(mm)
1
2
3
4
5
Calculation:
38
52
45
48
61
The following is the formula for standard error
Use the data from the previous example to find standard error.
Step 1: Calculate the square root the number of samples
Step 2: Divide the standard deviation by the square root of the number of samples.
Calculation:
You will need to be able to calculate standard deviation and standard error for the “Why Don’t Whales Have Legs” lab.