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Algebra I: Chapter 12 Notes
Probability and Statistics
Section 12-1, Day 1
Population –
Sample –
Simple Random Sample –
Bias –
Section 12-1, Day 1
Population – all members of a group of interest
Sample – some members of a group of interest
Simple Random Sample – each member in the population
has the same chance of being chosen for the sample
Bias – an error because of misrepresentation of a
population
Section 12-1, Day 1
Other Types of Samples:
Systematic Sample
Self-Selected Sample
Convenience Sample
Stratified Sample
Section 12-1, Day 1
Other Types of Samples:
Systematic Sample
Self-Selected Sample
Members are selected using a
specific interval, such as every
third person
Members volunteer to be
included in the sample
Convenience Sample
Stratified Sample
Members are easy to reach for
the sample
The population is first divided
into groups, then members of
each group are randomly chose
for the sample
Section 12-1, Day 1
Example: Animals in a zoo are divided by
species. Then two animals are selected at
random from each group to have their blood
tested.
a) Identify the sample and population
b) Classify the sample as simple, systematic,
convenience, or stratified. Explain.
Section 12-1, Day 1
Example 2: Identify each sample as biased or
unbiased
a) Every 5th person coming into a grocery store
is asked to name their favorite radio station.
b) Every 5th person at the country music
showcase is asked to name their favorite
radio station
Section 12-1, Day 2
Study Types
Type
Definition
Example
Survey
Data are collected from responses
from a sample regarding:
Asking students for their
opinions on dance
decorations
Observation Members of a sample are observed…
al Study
A gaming company
watches a group of teens
play a video game
Experiment
A teacher gives one
Algebra class a pencil and
paper test, and the other
class a computer test
covering the same
information
The sample is divided into 2 groups:
• An experimental group:
• A control group:
Section 12-1, Day 2
Study Types
Type
Definition
Example
Survey
Data are collected from responses
Asking students for their
from a sample regarding:
opinions on dance
Characteristics, behaviors, or opinions decorations
Observation Members of a sample are observed…
al Study
Without being affected by the study
A gaming company
watches a group of teens
play a video game
Experiment
A teacher gives one
Algebra class a pencil and
paper test, and the other
class a computer test
covering the same
information
The sample is divided into 2 groups:
• An experimental group: Undergoes
change
• A control group: does not undergo
change
Section 12-1, Day 2
Ex) Determine whether each situation is a survey, an
observational survey, or an experiment. Explain
a) A local charity is interested in finding out if residents would
use a curb-side service for donations. They distribute 30
questionnaires to people in the neighborhood.
a) A company shows 5 different commercials that advertise the
same product. They record the students reaction to each.
Section 12-1, Day 2
Ex) Identify each survey question as biased or
unbiased. If biased, explain
a) Is your favorite ice cream plain vanilla or
delicious chocolate?
b) What types of reading material(s) do you
enjoy?
Section 12-2, Day 1
Statistical Inference –
Statistic –
Parameter –
Section 12-2, Day 1
Statistical Inference – using statistics to draw
conclusions
Statistic – measure that describes a characteristic of
a sample
Parameter – a measure that describes a
characteristic of a population
Section 12-2, Day 1
Ex) Identify the sample and population. Then describe
the sample statistic and the population parameter.
a) At a local university, a random sample of 40
scholarship applicants is selected. The mean GPA of
the 40 applicants is calculated.
b) A stratified random sample of registered nurses is
selected from all hospitals in a 3-county area, and
the median salary is calculated.
Section 12-2, Day 1
Mean Absolute Deviation (MAD): The average of
the absolute values of the differences between
the mean and each value in the data set.
The MAD predicts errors and and judges how
well the mean represents the data.
Section 12-2, Day 1
Finding the MAD:
1) Find the mean ( x )
2) Find the absolute value
of the difference of each
data value and the mean
3) Find the sum of the
values in step 2
4) Divide the sum by the
number of values in the
data set
Find the MAD of the set
{2, 2, 3, 4, 14}
Section 12-2, Day 2
Standard Deviation – shows how the data
deviate from the mean. Represented by the
lowercase Greek symbol sigma σ
Variance – the square of standard deviation
s
2
Section 12-2, Day 2
Standard Deviation
1) Find the mean
2) Find the square of the
difference between each
data value and the mean
3) Find the sum of the
values in step 2 (x - x )2
n
4) Divide the sum by the
number of values
5) Take the square root of
the number in step 4
Find the standard
deviation and variance of
the data set:
{9, 10, 11, 6, 9, 11, 9, 8,
11, 8, 7, 9, 11, 11, 5}
Section 12-2, Day 2
Cont…Find the standard deviation and variance
of the data set: {9, 10, 11, 6, 9, 11, 9, 8, 11, 8, 7,
9, 11, 11, 5}
Section 12-3, Day 1
Distribution of Data
Section 12-3, Day 1
Ex1) Use the data to construct a histogram for
the data, and describe the shape of the
distribution
{25, 22, 31, 25, 26, 35, 18, 39, 22, 32, 34, 26, 42,
23, 40, 36, 18, 30, 26, 30, 37, 23, 19, 33, 24, 29,
39, 21, 43, 25, 34, 24, 26, 30, 21, 22}
Use this page for your histogram
Section 12-3, Day 1
Ex2) Use the data to construct a histogram for
the data, and describe the shape of the
distribution
{9, 17, 15, 10, 16, 2, 17, 19, 10, 18, 14, 8, 20, 20,
3, 21, 12, 11, 5, 26, 15, 28, 12, 5, 27, 26, 15, 53,
12, 7, 22, 11, 8, 16, 22, 15}
Use this page for your histogram
Section 12-4, Day 1: Transformation of
Data
Ex1) Find the mean, median, mode, range, and standard deviation of
the data set {13, 5, 8, 12, 7, 4, 5, 8, 14, 11, 13, 8}
Mean:
Median:
Mode:
Range:
SD:
Section 12-4, Day 1: Transformation of
Data
Now add 7 to each value and find the mean, median, mode, range and
standard deviation of the data set from the previous slide {13, 5, 8, 12, 7, 4,
5, 8, 14, 11, 13, 8}
Mean:
Median:
Mode:
Range:
SD:
Section 12-4, Day 1
If a number k is added or subtracted to every
value in the data set, what happens to the:
Mean:
Median:
Mode:
Range:
Standard Deviation:
Section 12-4, Day 1: Transformation of
Data
Ex1) Find the mean, median, mode, range, and standard deviation of
the data set {21, 12, 15, 18, 16, 10, 12, 19, 17, 18, 12, 22}
Mean:
Median:
Mode:
Range:
SD:
Section 12-4, Day 1: Transformation of
Data
Now multiply each value by 3 then find the mean, median, mode,
range, and standard deviation of the data set {21, 12, 15, 18, 16, 10,
12, 19, 17, 18, 12, 22}
Mean:
Median:
Mode:
Range:
SD:
Section 12-4, Day 1
If a number k (when k > 0) is multiplied to every
value in the data set, what happens to the:
Mean:
Median:
Mode:
Range:
Standard Deviation:
Section 12-4, Day 1: Comparing Data
Below are quiz scores for two students, Kody and
Tori. On the next 2 slides you will construct a
histogram for each data set and describe the shape
of each distribution.
Kody: 85, 95, 70, 87, 78, 82, 84, 84, 85, 99, 88, 74,
75, 89, 79, 80, 92, 91, 96, 81
Tori: 89, 76, 87, 86, 92, 77, 78, 83, 83, 82, 81, 82,
84, 85, 85, 86, 89, 93, 77, 85
Use this page for your histogram
(Kody’s Quiz Scores)
Use this page for your histogram:
(Tori’s Quiz Scores)
Section 12-4, Day 1
Using the quiz data, compare the mean and
standard deviation for Kody and Tori.
Kody
Tori
Mean:
Mean:
Standard Deviation:
Standard Deviation: