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Standard Deviation Worksheet
Name_____________
What is standard deviation?
What does it tell us if an experiment had a low standard deviation?
What does it tell us if an experiment had a high standard deviation?
How do we calculate standard deviation?
Let's say we wanted to calculate the standard deviation for the amounts of gold coins pirates on a pirate
ship have.
There are 100 pirates on the ship. In statistical terms this means we have a population of 100. If we
know the amount of gold coins each of the 100 pirates have, we use the standard deviation equation
for an entire population:
What if we don't know the amount of gold coins each of the 100 pirates have? For example, we only
had enough time to ask 5 pirates how many gold coins they have. In statistical terms this means we
have a sample size of 5 and in this case we use the standard deviation equation for a sample of a
population:
The rest of this example will be done in the case where we have a sample size of 5 pirates, therefore
we will be using the standard deviation equation for a sample of a population.
Here are the amounts of gold coins the 5 pirates have:
1. Calculate the mean:
4, 2, 5, 8, 6.
2. Calculate
3. Calculate
for each value in the sample:
:
4. Calculate the standard deviation:
The standard deviation for the amounts of gold coins the pirates have is 2.24 gold coins.
This means…__________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
How to Calculate standard deviation for a data set. (Problems 1-8.)
Example Problems:
The Vancouver Canucks Hockey team played ten games. Find the standard deviation for the number of
points scored during those 10 games: 0, 4, 1, 2, 1, 3, 1, 5, 0, 2.
Follow the steps below to calculate the standard deviation.
Step 1: Average the scores in the Score column of the table below in order from the smallest to the largest.
Step 2: Find the mean of the data set and place your answer below on Line A.
Step 3: Subtract each of the scores from the mean. Record the difference in the Difference From The Mean
column in the table below. Be sure to record whether the answer is positive or negative. (i.e.:4-5=-1,7-5=2)
Step 4: Find the square of each number in the Difference From The Mean column and record the result in
2
the Square of the Difference column (i.e.: (1)  1)
Step 5:The number of items in the data set in labeled n. Record the number in this data set on Line B
below.
Step 6: Find the sum of the numbers in the Square of the Difference and record your answer in the table.
2
Step 7: Take the Sum of the (Difference from the Mean) and divide it by n. Record your answer on Line
C below.
Step 8: The square root of Line C is the standard deviation. Record your answer on Line D below:
Score
Difference from the mean
Difference from the mean2
0
-1.9
3.61
4
2.1
4.41
1
-.9
0.81
2
0.1
0.01
1
-.9
0.81
3
1
1.1
-.9
1.21
0.81
5
3.1
9.61
0
-1.9
3.61
2
0.1
0.01
Sum of (Difference from the
2
mean)
A. Mean:____1.9_________
B. n:_____10__________
2
C. Sum of (Difference from the Mean) divided by (n):___2.49____
D. Standard deviation ( diff . fromMean)
2
is_______1.58________
24.9
Standard Deviation: Calculate standard deviation for the following data sets.
1. Find the standard deviation for the following test scores.
A. Mean:_____________
84, 100, 84, 68, 84, 100, 84
B. n:_______________
2
C. Sum of (Difference from the Mean) divided by (n):_______
D. Standard deviation ( diff . fromMean)
2
is_______________
2. Find the standard deviation for the following masses of students (in kg): 70, 52, 68, 60, 59, 72, 55, 58,
66, 69, 72, 61.
A. Mean:_____________
B. n:_______________
2
C. Sum of (Difference from the Mean) divided by (n):_______
D. Standard deviation ( diff . fromMean)
2
is_______________