12.4 Standard Deviation
Let's assume that each
person has an equal
opportunity, not to become
equal, but to become
different. To realize
whatever unique potential
of body, mind and spirit
he or she possesses.
Tree Diagrams
Ex 7) A student made the following observations
of the weather in his hometown.
• On 28% of the days, the
sky was mostly clear.
• During the mostly clear days, it
rained 4% of the time.
• During the cloudy days it
rained 31% of the time.
a. Use a tree diagram to find the probability that a day will start out
clear, and then it will rain.
b. Find the probability that it will not rain on any given day.
Standard Deviation
Range: The difference between the greatest and least values of
a data set.
Interquartile Range (IQR): The difference between the 3rd
and 1st quartiles.
Standard Deviation: How much the values in a data set vary
from the mean.
***The smaller the standard deviation, the closer all of the
numbers are to the mean
Standard Deviation
Determining Standard Deviation:
1) Find the mean of the data set: x
2) Find the difference between each value and the mean: x  x
3) Square each difference:  x  x 
2
 x  x 
4) Find the average of these squares:
n
2
 x  x 
5) Take the square root to find standard deviation:  
n
2
Standard Deviation
Ex1) There are 9 members of the Community Youth Leadership
Board. Find the mean, median, range, interquartile range, and
standard deviation of their ages: 22, 15, 24, 17, 16, 25, 20, 19, 26.
Finding Standard Deviation with the Calculator
Ex2) Use a graphing calculator to determine the standard deviation
of our previous data set: 22, 15, 24, 17, 16, 25, 20, 19, 26.
Using the Standard Deviation
Ex 3) The number of points that Darden scored in each of 11 basketball
games is listed below. Within how many standard deviations of the mean
do all of the values fall? What can Darden’s coach do with this
information? 8, 12, 13, 10, 7, 5, 10, 9, 13, 11, 8
Step 1: Determine
mean and standard
deviation.
Step 2: Draw a
number line. Plot
the data values and
the mean.
Step 3: Mark off
intervals of 2.4
on either side of
the mean.
12.4 Standard Deviation
Let's assume that each
person has an equal
p. 656 9 – 13 all
opportunity, not to become
equal, but to become
p. 672 #1, 2, 4 (do
different. To realize
these 3 by hand),
whatever unique potential
8, 9, 15, 17-19
of body, mind and spirit
he or she possesses.