Transcript Probability and Statistics

PROBABILITY AND STATISTICS
Unit 6
Denise Keen
STUDENT OBJECTIVES – DAY ONE

Students will…


Interpret real world problems and create tables of
related number pairs (vertical or horizontal) with
appropriate labels with 95% accuracy.
X
2
4
6
8
Y
0
1
2
3
Construct a line graph representing the related
number pairs with appropriate labels with 95%
accuracy. 4
3
2
1
0
2
4
6
8
STUDENT OBJECTIVES – DAY TWO

Students will…

Interpret data and tables to determine mean,
median, mode, and range with 90% accuracy.

Describe and (and calculate with step by step
instructions) the process of determining mean,
median (given an even number and an odd number of
data), mode (can be none or more than one mode),
and the range of a given data set with 90% accuracy.
62, 72, 75, 85, 88, 89, 90, 92, 99
mean: (62+72+75+85+88+89+90+92+99) ÷ 9 = 83.5
median: 88
mode: none
range: 99 – 62 = 37
STUDENT OBJECTIVES – DAY THREE

Students will…

Interpret how changing data within a given data set
will affect the mean, median, mode, or range with
90% accuracy.
62, 72, 75, 85, 88, 89, 90, 92, 99, 99
mean: 83.5, 91.25
median: 88, 88.5
mode: none, 99
range: 99 – 62 = 37, 99 – 62 = 37

Construct graphs (vertically and horizontally) with
Microsoft Excel using appropriate labels, scale, and
key such as: bar graphs, line graphs, and double bar
graphs with 100% accuracy.
STUDENT OBJECTIVES – DAY FOUR

Students will…

Justify a selection of graphical representation using
appropriate mathematical vocabulary for given data
with 95% accuracy.
Favorite Colors
Blue 20%
Red 30%
Yellow 15%
Green 35%

Evaluate numerous graphical representations of the
same data to select the best representation with 95%
accuracy.
WHAT IS PROBABILITY?
Mathematics definition – the likelihood that
an event will occur, expressed as the ratio of the
number of favorable outcomes in the set of
outcomes divided by the total number of possible
outcomes.
 General definition – the likelihood (possibility)
of something happening.


Example: the probability of rolling a “2” with a
die is 1 out of 6
WHAT ARE STATISTICS?
Mathematics definition – the collection,
organization, analysis, and interpretation of data
collected during a study.
 General definition – data that is collected,
organized, and interpreted that shows individual
preference or outcome with regards to a question
or event.


Example – Favorite colors: 20 students prefer
blue, 30 students prefer red, 15 students
prefer yellow, and 35 students prefer green.
MEAN
Mean is the average of a set of numbers (values).
 To calculate the mean:

1.
2.
Add up all of the numbers
Divide by how many numbers there are
15, 26, 24, 30, 18, 10, 17
1.
2.
15 + 26 + 24 + 30 + 18 + 10 + 17 = 140
140 ÷ 7 = 20
MEDIAN
Median is the “middle” number (value) in a
sorted (least to greatest) list of numbers.
 To find the median:

1.
2.
Place the numbers in order from least to greatest
Find the middle number
15, 26, 24, 30, 18, 10, 17
1.
2.
10, 15, 17, 18, 24, 26, 30
10, 15, 17, 18, 24, 26, 30
MODE
Mode is the number (value) that occurs most
often in a data set
 To determine the mode:

1.
2.
3.
1.
2.
Place the numbers in order from least to greatest
Count how many there are of each number
There may be one mode, more than one mode, or no
mode at all
19, 8, 29, 35, 19, 28, 15
8, 15, 19, 19, 28, 29, 35
Since 19 appears twice, the mode is 19
RANGE
Range is the difference between the largest and
smallest numbers (values).
 To calculate the range:

1.
2.
Place the numbers in order from least to greatest.
Subtract the smallest number from the largest
number.
19, 8, 29, 35, 19, 28, 15
1.
2.
8, 15, 19, 19, 28, 29, 35
35 – 8 = 27
HOW WILL I EVER REMEMBER THE
DIFFERENCE????

Mode, Median, Mean and Range song
http://www.songsforteaching.com/math/modemedianmeanandrange.
php
LYRICS
You’ve got mode, median, mean and range
Mode, median, mean and range,
Don’t you think these words sound strange?
Don’t you think these words sound strange?
I will get your mind to change!
MODE, mode, m-m-m-mode, mode,
It’s the number that occurs, occurs the most, most,
Singin’ mode, mode, m-m-m-mode, mode,
It’s the number that occurs, occurs the most, most!
You’ve got: 1, 2, 2, 3, 3, 3, 4 -- 1, 2, 2, 3, 3, 3, 4
Which of those numbers did I say more?
Which of those numbers did I say more?
3 is the mode, cuz it occu-u-u-rs the MOST!
[repeat stanza]
Now, STOP! Let’s take it to the middle,
Gonna find the MEDIAN, no time to daddle-diddle.
Line up all the numbers from the smallest to the big
And the one that’s in the middle does the median jig.
“Go median, middle number, Go median, middle number.”
LYRICS
Now the third one’s MEAN, not nice, but mean,
It’s the av-er-age number if you know what I mean.
You just: add up all the numbers and divide it by the number of
addends.
What’s that? What’s MEAN?
You add up all the numbers and divide it by the number of addends.
Ya, you know what I mean?
You add up all the numbers and divide it by the number of addends.
It’s the av-er-age number!
Mean: it’s the average number!
One more round, then the song is done.
Let’s talk about RANGE and have some fun.
It’s the biggest number, minus the smallest number – in the group, in
the group.
It’s the biggest number, minus the smallest number – in the group, in
the group.
You’ve got mode, median, mean and range
Mode, median, mean and range,
Don’t you think these words sound strange?
Don’t you think these words sound strange?
I just got your mind to change!
CREATING AND IMBEDDING A GRAPH
Line Graph
25
20
15
10
5
0
2009
2010
2011
2012
LINE GRAPH
1.
2.
3.
4.
5.
6.
7.
8.
9.
Open Microsoft Excel
Open data table template in “Keen” folder
Input the data for your graph
Click on the Rows of data you wish to include
in the line chart.
Click on the Insert tab in the Office Ribbon.
Click on the Line button in the Charts group.
Select the first line graph option
Click and drag graph to move location
Click on corner and slide to change size
CREATING AND IMBEDDING A GRAPH
Bar Graph
25
20
15
10
5
0
Math
Science
Social
Studies
Language
Arts
BAR GRAPH
1.
2.
3.
4.
5.
6.
7.
8.
9.
Open Microsoft Excel
Open data table template in “Keen” folder
Input data for your graph
Click on the Rows of data you wish to include
in the line chart.
Click on the Insert tab in the Office Ribbon.
Click on the Bar button in the Charts group.
Select the first bar graph option
Click and drag graph to move location
Click on corner and slide to change size
CREATING AND IMBEDDING A GRAPH
Double Bar Graph
Track
Soccer
Girls
Boys
Basketball
0
10
20
30
DOUBLE BAR GRAPH
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
Open Microsoft Excel
Open data table template in “Keen” folder
Input data for your graph
Click on the Rows of data you wish to include
in the line chart.
Click on the Insert tab in the Office Ribbon.
Click on the Bar button in the Charts group.
Select the All Chart Types option
Select Bar option
Select first bar option
Click and drag graph to move location
Click on corner and slide to change size
CHOOSING THE MOST APPROPRIATE
GRAPH FOR THE DATA

When to use a line graph…


When to use a bar graph…


Line graphs are used to show change in data over
time
Bar graphs are used to show comparisons among
categories
When to use a double bar graph…

Double bar graphs as used to category comparisons
among more than one group