Warm-up:
1. Which statement is false?
a) The teacher with the least number of years teaching is female.
b) The range in the years teaching is greater for male teachers than for female teachers.
c) The difference in the maximum number of years teaching for male and female teachers is
1.
d) The median number of years teaching for female teachers is 2 less than the median for
male teachers.
Evaluate each expression.
2. |-9|
3. (6)2
4. (x – 3)2 when x = -5
5. |2x + 7| when x = -9
Use a calculator to evaluate each expression.
6. √36
7. 360.5
What pattern do you notice in #6-9?
8. √81
9. 810.5
Standard Deviation Notes
Students in Mrs. Smith’s Communication Club are interested in how many hours they spend
watching television. They collected the following data which shows the number of hours they
each watched television in one week.
3, 8.5, 9, 9, 12.5, 14, 16.5, 18, 19, 20.5
What are some ways you could analyze this data set?
(Remember what we’ve been talking about the last two blocks!)
Mean, median & mode are measures of _________________________________
Range is a measure of ____________________________
Let’s compare each element in the data to the mean of the data. How would we find the
distance of each element from the mean? __________
x
3
8.5
9
x-μ
x – μ shows the deviation for each point in the data
set. Now find the average difference from the mean…
Average x – μ’s for our data set =
(i.e. average deviation)
9
12.5
14
16.5
18
19
20.5
Will this always happen?
Why?
x
x-μ
3
-10
8.5
-4.5
9
-4
9
-4
12.5
-0.5
14
1
16.5
3.5
18
5
19
6
20.5
7.5
|x – μ|
|x – μ| shows the deviation for each point in the data
set, without taking the direction of the data point into
account.
Now find the average distance from the mean…
Average distance from the mean =
(i.e. Mean Absolute Deviation)
Sum =
Mean Absolute Deviation:
n
 x 
i 1
i
n
, where
μ = the mean of the data set
n = the number of elements in the data set
xi = the ith element of the data set
Questions:
1. What does a high value for mean absolute deviation indicate?
2. What does a low value for mean absolute deviation indicate?
Another method for dispersion utilizes _________________________ to make the
deviations (x – μ) positive.
x
x-μ
3
-10
8.5
-4.5
9
-4
9
-4
12.5
-0.5
14
1
16.5
3.5
18
5
19
6
20.5
7.5
(x – μ)2
Now find the average of (x – μ)2.
This value is the variance. Its symbol is ____
Sum =
Variance (σ2):
n
 
2
 x   
i 1
2
i
n
μ = the mean of the data set
, where
n = the number of elements in the data set
xi = the ith element of the data set
Question:
1. What were the units on the variance of our data set?
2. How can we get the units to be the same as the original data set?
Standard Deviation (σ):
n

  xi   
2
i 1
n
, where
μ = the mean of the data set
n = the number of elements in the data set
xi = the ith element of the data set
Try it out! Which data set has the smallest standard deviation?
A
B
C
1, 2, 3, 4, 5, 6, 7
1, 1, 1, 4, 7, 7, 7
1, 4, 4, 4, 4, 4, 7
Summary:
 Statisticians like to measure the dispersion (spread) of the data set about the mean in order
to help make inferences about the population.

Range:

Mean Absolute Deviation:

Variance:

Standard Deviation:
FYI: Mean Absolute Deviation is less affected by outlier data than standard deviation or variance.
Homework for Standard Deviation
1. On six consecutive Sundays, a tow-truck operator received 9, 7, 11, 10, 13, and 7 service calls. Calculate
the standard deviation.
Find the mean (   x ). Round to the nearest hundredth.
Data
Deviations x  
x
  x  _____________
Squared Deviations  x   
2
9
7
11
10
13
7
SUM = ___________
Variance =  2 
SUM

6
The standard deviation is the square root of the variance.
Standard Deviation =    2  _______
2. The following are the wind velocities reported at an airport at 6 p.m. on eight consecutive days: 13, 8, 15,
11, 3, 10, 12, and 8 miles per hour. Calculate the standard deviation.
Find the mean ( x ). Round to the nearest hundredth.   x  _____________
Data
Deviations x  
x
Squared Deviations  x   
2
SUM = ___________
Variance =  2 
SUM

8
The standard deviation is the square root of the variance. Standard Deviation =    2  _______
3. Heights of adult males have a mean of 69 and a standard deviation of 2.8 inches. Basketball player Michael
Jordan earned a giant reputation for his skills, but at a height of 78 inches, is he exceptionally tall when
compared to the general population of adult males? Find the z-score for his height. Interpret the result.
4. The following set of data represents the salaries (in millions) of the 10 highest paid athletes in Major
League Baseball in the 2003 season.
22,
20,
18.7,
17.2,
16,
15.7,
15.7,
15.6,
15.6,
15.5
a) What is the mean of the salaries? Round to the nearest tenth and use units in your answer!
b) What is the standard deviation of the salaries of these 10 players?
Data
Deviations x  
x
Squared Deviations  x   
2
SUM = ___________
Variance =  2 
SUM

10
The standard deviation is the square root of the variance. Standard Deviation =    2  _______