Amanda has taught high school science for over 10 years. They have a Master's Degree in Cellular and Molecular Physiology from Tufts Medical School and a Master's of Teaching from Simmons College. They also are certified in secondary special education, biology, and physics in Massachusetts.
Algebra I Assignment - Calculating Probabilities & Applying Statistical Concepts
Assignment Explanation and Topic Overview
In this assignment students will be learning about independent and dependent events and calculating the probability. They will also calculate the mean, median, mode, and range for a given set of numbers, as well as use tables and schedules to organize and analyze data and read graphs and pie charts. To demonstrate their learning students will solve sample problems by creating an investigation and collecting data to analyze.
Key Terms
- Independent event: An event that does not depend on the events prior to it
- Dependent event: An event that does depend on another prior event
- Mean: The average of a set of numbers
- Median: The middle number of a set of numbers
- Mode: The most common number in a set
- Range: The difference between the lowest to highest value in a set
- Table: A method of organizing data into columns and rows
- Schedule: A method of organizing data according to time
- Pie chart: A method of organizing data according to percentages
- Line graph: A method of organizing data as it changes over time
- Bar graph: A method of organizing data to compare quantities or frequencies
Required Materials
- Calculator
- Pencil and paper
- Poster paper and colored pencils
- Ruler
- Graph paper (optional)
Review for Students
Probability
Independent events are those that occur without any prior event. For example, if I were to calculate the probability of rolling a six two times in a row, these are independent events. Since there are six sides on the dice, the probability for each event is 1/6. To calculate the total probability we multiply them together: 1/6 * 1/6 = 0.027
A dependent event is an event where the second instance is affected by the first. Imagine pulling cards from the deck. The probability of pulling an ace is four out of 52 cards. To pull two aces in a row however without resetting the deck changes the second probability to three out of 51 cards. Thus, the total probability is: 4/52 * 3/51 = 0.0045
Data and Graphing
Data can be organized through a variety of characteristics such as the mean, median, mode or range. Let's look at a sample set of data: 3, 3, 5, 6, 7, 3, 7
The mean is the average, meaning we add all the numbers together and divide by the total:
(3 + 3+ 5 + 6 + 7 + 3 + 7) / 7 = 4.8
The median can be found by arranging the numbers in numerical order and selecting the middle value. 3, 3, 3, 5, 6, 7, 7. So, the median is 5.
The mode is the most common number, which is 3 in this set. Lastly, the range is the difference between the highest and lowest value in a set. Here, we get: 7 - 3 = 4.
Tables can be used to organize data into rows and columns. For example, if you collected information about the height of plants over a seven day period this information could be organized into a table as follows:
Day | Height |
---|---|
1 | 2.3' |
2 | 2.3' |
3 | 2.5' |
4 | 2.6' |
5 | 2.8' |
6 | 3.1' |
7 | 3.4' |
Schedules are used to organize events in time. For example a schedule can be utilized to organize the times at which different tasks need to be completed in an experiment. Using our plant example from above, a possible schedule might look like:
Day | Time | Task |
---|---|---|
Monday | AM: PM: |
Water plants Measure plants |
Tuesday | PM: | Measure plants |
Wednesday | AM: PM: |
Water plants Measure plants |
Thursday | PM: | Measure plants |
Friday | AM: PM: |
Water plants Measure plants |
Saturday | PM: | Measure plants |
Sunday | AM: PM: |
Water plants Measure plants |
The data in tables can be used to create graphs and pie charts. Pie charts show the percentage of each of the variables in a circle, whereas bar and line graphs show how a variable changes, either over time or by manipulating another variable. In a graph, the dependent variable you measure goes on the y (sideways) axis and the independent variable you manipulated, like time or amount of water, goes on the x axis (bottom).
Instructions for Students
Now that you've had a chance to review, it's time for you to complete some practice problems.
1. Find an example of independent and dependent events and create a poster showing the difference. Then, show your calculations for the probability of an independent and dependent event.
2. Use your environment to collect a set of data. You might choose to measure the height of flowers in your yard, the number of swings in different parks around town, or even the number of pencils in each room in your house. With your set of data, determine the mean, median, mode and range.
3. Next, organize your data from your investigation in step 2 into a table or schedule, depending on what kind of data you selected.
4. Lastly, create a graph of your data. Write a small summary of what the data means and your conclusions.
Rubric
Criteria for Success | Score (0-10 points) |
---|---|
Poster correctly demonstrates the difference between independent and dependent events | |
Poster correctly shows how to calculate the probability of independent and dependent events | |
At least 10 data points are collected for question 2 | |
Mean, median, mode and range are calculated for the data set | |
Data is organized in a table or schedule correctly | |
A line or bar graph is created with the data that includes the correct labels on the axes, title and units | |
Total | /60 |
Answer Key
1. A correct poster would explain that the difference between an independent and dependent event is that an independent event's probability does not depend on any other events. The calculations might include the same numbers for the independent events, but different numbers for the dependent events.
2. The specific calculations will depend on the data the student collects. However, the mean is the average of the data, the median is the middle number when the data is organized numerically, the mode is the most commonly occurring number and the range is the difference between the highest and lowest value.
3. A correct table will have a header for each column and data organized according to time or another logical format. All data should include units.
4. A proper graph has the independent variable on the x axis and the dependent variable on the y axis, includes a title and has units. The specific way the graph looks will depend on what data the student has collected.
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BackAlgebra I Assignment - Calculating Probabilities & Applying Statistical Concepts
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