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## Probability and Statistics

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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.
- Construct a line graph representing the related number pairs with appropriate labels with 95% accuracy.

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:
- Add up all of the numbers
- Divide by how many numbers there are

15, 26, 24, 30, 18, 10, 17

- 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:
- Place the numbers in order from least to greatest
- Find the middle number

15, 26, 24, 30, 18, 10, 17

- 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:
- 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:
- Place the numbers in order from least to greatest.
- Subtract the smallest number from the largest number.

19, 8, 29, 35, 19, 28, 15

- 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 rangeMode, 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, 4Which 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 bigAnd 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 rangeMode, 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

Line Graph

- Open Microsoft Excel
- Open data table template in “Keen” folder
- Input the data for your graph
- Click on the Rowsof data you wish to include in the line chart.
- Click on the Insert tab in the Office Ribbon.
- Click on the Linebutton in the Chartsgroup.
- 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

Bar Graph

- 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 Barbutton 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

Double Bar Graph

- 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 Barbutton 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…
- Line graphs are used to show change in data over time
- When to use a bar graph…
- 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

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