Transcript 92The_Mean_and_the_Standard Deviation

Chapter 9 Probability Distributions
9.2
MATHPOWERTM 12, WESTERN EDITION 9.2.1
The Mean
The mean, which is one of the three averages of a set of numbers,
is the sum of all the numbers in the set divided by the number of
numbers. For the set of data values x1, x2, x3, …, xn:
Example: Determine the mean of the following set of math marks:
53, 68, 41, 79, 82, 35, 92, 65, 68, 73, 54
9.2.2
The Standard Deviation
The Standard Deviation is the measure that describes how much
variation there is among all the data values in a set of data and
the mean of the data.
Example: Determine the standard deviation for the following
set of math marks: 53, 68, 41, 79, 82, 35, 92, 65, 68, 73, 54.
9.2.3
Using the Graphing Calculator to Calculate Standard Deviation
1. Press [STAT] [ENTER].
2. Enter the data into the list.
3. Press [STAT] [
] [Enter].
Solution Screen
9.2.4
Finding Standard Deviation
Find the mean and the standard deviation
for the following two sets of data:
X1 X2 X3 X4 X5 X6 X7 X8 X9
A
13 16 14 15 14 16 17 15 15
B
14 12 11 15 13 17 18 16 14
x

9.2.5
Z-Scores
A z-score is a value which describes how many standard deviations
above or below the mean a particular data value falls.
A positive z-score indicates that the data value is above the mean.
A negative z-score indicates that the data value is below the mean.
z-score
Example: The marks on a math test had a mean of 63 and
a standard deviation of 6. Bob scored 82. Find his z-score.
9.2.6
Z-Scores
Every Grade 12 student in the school district wrote four exams.
The results were normally distributed. Consider all the data
in the table below. In which subject did Tom ranked highest?
Math
Standard Tom’s
Mean Deviation Score
62
3
71
Chemistry
73
4
83
Biology
57
7
62
Physics
68
6
76
9.2.7
Z-Scores [cont’d]
Math
x
zx 

Chemistry
x
zx 

Biology
x
zx 

Physics
x
zx 

Using z-scores to compare marks in the four subject areas,
Tom ranked highest in
9.2.8
Z-Scores
The marks on an examination were normally distributed with
a mean of 54 and a standard deviation of 12. A decision was
made to adjust the original marks but leave z-scores unchanged.
This was done by raising the mean to 64 while reducing the
standard deviation to eight. If the original mark was 36%,
what is the corresponding adjusted mark?
zx 
x

zx 
x

The adjusted mark
would be
9.2.9
Suggested Questions:
Pages 412 and 413
1-4, 7
9.2.10