Curriculum Index Curriculum Objectives Curriculum Outline Student Pages Virginia SOLs Lesson 1: Preparing For Your Journey Lesson 2: Meet Your Ship Lesson 3: Plotting The Course Lesson 5: Environmental Impact Bibliography

LESSON 4: ADDING IT UP

Objectives
Materials
Background Information
Key Questions
Vocabulary
Procedure
Evaluation

Objectives

  • Students will determine total distance traveled.
  • Students will create a spreadsheet and bar graph using the various distances traveled.
  • Students will determine mean, median, mode and range of distance traveled.
  • Students will utilize problem solving skills to determine if their ship encountered stormy or foggy weather.
  • Students will utilize problem solving skills to form a hypothesis about why low daily travel distances occurred.

Materials

  • Completed Wind Barb Calculation sheet from Lesson 3
  • Printable Circular Protractor (6 per sheet)
  • Graph Paper Handout (6 graphs per sheet)
  • Completed Atmospheric Pressure-Dew Point Worksheet from Lesson 3
  • Highlighter
  • Captain's Log with distance traveled for each data point
  • Calculator
  • Computer Access with Spreadsheet Software

Background Information

Review Lesson One for Wind Barb and Atmospheric Pressure Procedures

Mean, Mode, Median and Range

There are 4 terms in statistics that we need to understand. Mean, mode, median and range. Most of us know how to find an average. We want to know what our grade is for the semester so we add up all of our tests and divide that number by how many tests we've taken. We use the term average, but in statistics it is called the mean.

Mean

Example:

Five tests results: 85, 88, 99, 75, 82
85 + 88 + 99 + 75 + 82 = 429
Divide 429 by 5: 85.8

The mean is 85.8

The mean of a set of numbers may not reflect the true average. Suppose we learn that the mean annual income of a certain neighborhood is 1 million. We might assume that everyone that lives in this neighborhood is rich. In fact, most of those who live in this neighborhood are poor and there is one rich person who is a multi-millionaire. This throws the average off because there is one large number mixed in with a lot of smaller ones.

By looking at the mean and the median, we get a better look at how the numbers are spread out. With one really wealthy person living in the neighborhood, the median will be low.

Median

The median is the "middle value" in a list. The first thing to do is put the numbers in order from lowest to highest. When the list has an odd number of entries, the median will be the number in the middle. When the list has an even number of entries, add the two middle numbers together and divide by two to find the median.

Examples:

5 Items - odd amount of numbers
Find the Median of: 8, 12, 66, 14, 11
Put the numbers in order: 8, 11, 12, 14, 66 (lowest to highest)
The Median is: 12 (The number in the middle)

6 Items - even amount of numbers
Find the Median of: 8, 12, 66, 14, 16, 10
Put the numbers in order: 8, 10, 12, 14, 16, 66 (lowest to highest)
Add the 2 middle numbers then divide by 2: 12 + 14 = 26 ÷ 2 = 13
The Median is 13.

Mode

The mode can help to explain the data even further. The mode is the number that repeats most often.

If we are told that the mean of four numbers is 51 with a median of 50, it might be natural to assume that the numbers are all very close in value. Let's look at the data to see if this is correct:

102  98  2  2

The mean is (102 + 98 + 2 + 2)/4 = 204/4 = 51 and the median = (98+2)/2 = 50. The mode is 2 since it is repeated most often. This tells us that with a mean of 51 and a median of 50 that there had to be some large and small numbers in the set instead of all of the numbers being very close in value.

Examples:

Find the mode of:
7, 2, 2, 43, 16, 10, 43, 14, 14, 14, 22, 35, 6
Put the numbers in order:
2, 2, 6, 7, 10, 14, 14, 14, 16, 22, 35, 43, 43
The Mode is 14 (14 occurs the most at 3 times)

There can be more than one mode. There can also be no mode if no number repeats.

Range

The range is simply the difference between the largest and smallest number. Largest number - smallest number = range.

Example:

Find the range of:
9, 3, 44, 15, 6
Put the numbers in order:
3, 6, 9, 15, 44
The range would be 44 - 3 = 41. Your range is 41.

Weather Data

Warnings of adverse weather and the ability to forecast weather at sea help seagoing vessels reach their destinations safely.

Knowledge of ocean winds allow ship captains to decide which route to take that will avoid strong headwinds and heavy seas that could slow the ship's progress, increase fuel consumption or risk damage to the ship or loss of life and cargo.

In winds that are below 20 knots, light winds, ships will lose speed if they are sailing into the wind and gain a little speed if the wind is a tail wind. For winds greater than 20 knots, the ship will lose speed no matter the direction of the wind because the wave action is increased. Additionally, high wind speeds will have a greater impact on a cargo ship that is loaded with cargo containers than it will on a tanker due to the cargo ship having a higher profile above the water.

Fog doesn't necessarily affect the ship's performance but it does hamper its progress. In areas of high fog, visibility is reduced. This causes the ship's captain to run at a reduced speed which in turn increases fuel consumption and takes the ship a longer period of time to make port.

A ship's captain needs to be able to interpret the meaning of air pressure readings in order to avoid the effects of adverse weather and high seas that are associated with low pressure systems.

Low pressure systems that generate winds weaker than gale intensity (less than 34 knots) are generally not a problem for ships. A weak system could however create rough seas for an extended period of time.

Gale force winds, 34-47 knots, and storms, winds higher than 48 knots create very rough seas in the open ocean. This causes the ship's captain to reduce the speed of the ship in order to protect crew and cargo.

Key Questions

  1. What affect does wind speed and direction have on waves?
  2. Why does dropping air pressure indicate an approaching storm?
  3. Why is it not enough to just know the average or mean of a set of numbers?

Vocabulary

  • Mean - The mean is the arithmetic average - The sum of a list of numbers, divided by the total number of numbers in the list.
  • Median - The median is the number in the middle. In order to find the median, you have to put the values in order from lowest to highest, then find the number that is exactly in the middle
  • Mode - The mode is the value(s) that occurs most often.
  • Range - The range of a set of numbers is the largest value in the set minus the smallest value in the set.
  • Bar Graph - Used to graphically present data that you have gathered.

Materials:

Procedure

Wind Speed and Direction of Wind

Materials:

  1. Hand out one circular protractor per student. There are six on one page to minimize the amount of paper needed to print.
  2. Hand out one cartesian graph sheet per student. There are six on one page to minimize the amount of paper needed to print.
  3. Have students cut out the circular protactor including the area in the middle. Leave the bar in the middle.
  4. Students will refer to the Wind Barb Calculation sheet from Lesson 3.
  5. Students will construct wind barbs from their data based on what they learned in Lesson One.
  6. Have your students label the 4 cardinal directions on the cartesian graph. North is always at the top.
  7. Explain to students that the halfway point between N and E (45º from N) is NE. 135º from N is SE. 225º from N is SW. 315º from N is NW.
  8. The wind direction from the data collected is listed in degrees, for example, 230.
  9. Have your students place the protractor on the cartesian graph such that 0º is positioned over N and the small hash mark in the center of the protractor is parallel to the horizontal line of the cartesian graph.
  10. There are two "0" marks on the protractor. In order to have the degrees read in a clockwise direction, position the hash mark in the center bar on the left side of the protractor. You can also explain the reading 180 over 0 should be at the top. Students will use the inner set of numbers.
  11. In order to draw a wind barb that has a direction of 230, students should locate 230º on the protractor and draw a line from the origin of the graph to the 230º mark. See Example
  12. The student will now reproduce the wind barb and add the feathers that denote wind speed in the Wind Barb Calculation sheet next to the recorded data for that point and continue for all data points.
  13. The student will also list the cardinal direction for the wind barb.

Atmospheric Pressure

Refer to Lesson One to refresh student's memories.

Materials:

  • Completed Atmospheric Pressure-Dew Point Worksheet from Lesson 3
  • Highlighter
  1. Students will highlight significant areas of changing pressure, either to a lower pressure or higher.
  2. The students will highlight conditions that are conducive to fog formation.
  3. Based on what they learned in Lesson One, students will write a short report on the types of weather their ship encountered and what impact it may have had on travel.
  4. Students can look at areas of low pressure, possible conditions of fog, and distance traveled for that time period to see if the weather had any impact. Low distances traveled will be a clue that it did.

Statistics

Materials:

  • Calculator One is provided here if you do not have access to calculators.
  1. Students will calculate total distance traveled, mean, median, mode and range for their data points.
  2. Students will list these values in their Captain's log.

Create a Bar Graph in Excel

Materials:

  • Microsoft Excel
  1. Download the finished product as an Excel file.
  2. Open a new spreadsheet in Excel.
  3. In cell A2 type the word Date.
  4. In cell B2 type the word Distance.
  5. In cell A3 type the date and time of the first reading. The first reading is at the bottom of the data sheet.
  6. In cell B3 type the distance traveled for that reading.
  7. Continue in this same manner for cells A4/B4, A5/B5 and so on until all data is entered. Example.
  8. Save the file using a naming scheme that your students will remember.
  9. Click the mouse on cell A2 and while holding the mouse button down, drag the mouse to highlight all of the data. Do not highlight any blank cells. Release the mouse button. All of the cells will turn a different color except for A2. This is normal. Example.
  10. Click on the Chart Wizard icon on the toolbar.
  11. Pick the Column chart type from the left panel. (This should already be highlighted by default.) Pick Clustered Column from the right panel. (This should already be highlighted by default.)Example
  12. Click Next.
  13. You will see an example of your bar graph in the top window of the dialog box. Example
  14. Click Next.
  15. Click on the titles tab at the top of the dialog box. In the Chart title box, type the title [Ship's Name] Daily Progress where [Ship's Name] is the name of the student's ship.
  16. As you type the title, it should be added to the preview window to the right. Example
  17. There are only two choices for where you want to place your bar graph: In the same sheet or in a new sheet. Click the radio button to place the graph as an object in sheet 1. Click Finish. Example
  18. The graph is placed in the spreadsheet. Example
  19. There are little lines in each days bar that represents the distance traveled during that time period. Place your mouse cursor over one of those areas and a pop up will display the data. Example
  20. Save the spreadsheet.
  21. Print the spreadsheet.
  22. Students may want to refer to this graph to determine if weather was a factor for days that have a low daily progress.

Evaluation

  • The student will be able calculate mean, median, mode and range.
  • The student will be able to utilize problem solving skills to determine the impact of weather on a ship's travel.
  • The student will be able to enter data into a spreadsheet and create a bar graph. (Students may also create line graphs, circle graphs, stem-and-leaf plots and box-and-whisker plots.)

Curriculum Index Curriculum Objectives Curriculum Outline Student Pages Virginia SOLs Lesson 1: Preparing For Your Journey Lesson 2: Meet Your Ship Lesson 3: Plotting The Course Lesson 5: Environmental Impact Bibliography

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