Textbook Question
What is the difference between a frequency polygon and an ogive?
2. Describing Data with Tables and Graphs
Frequency Distributions
2:00 minutesProblem 2.1.27c
Textbook Question
Use the ogive to approximate the
the number of black bears that weigh between 158.5 pounds and 244.5 pounds.
Verified step by step guidance1
Step 1: Understand the ogive graph. An ogive is a cumulative frequency graph that shows the cumulative number of observations below a certain value. The x-axis represents the weight of black bears, and the y-axis represents the cumulative frequency.
Step 2: Identify the cumulative frequency corresponding to the lower weight limit (158.5 pounds). Locate 158.5 on the x-axis and find the corresponding cumulative frequency on the y-axis by observing the graph.
Step 3: Identify the cumulative frequency corresponding to the upper weight limit (244.5 pounds). Locate 244.5 on the x-axis and find the corresponding cumulative frequency on the y-axis by observing the graph.
Step 4: Subtract the cumulative frequency at 158.5 pounds from the cumulative frequency at 244.5 pounds. This difference represents the number of black bears whose weights fall between 158.5 pounds and 244.5 pounds.
Step 5: Interpret the result. The difference calculated in Step 4 gives the approximate number of black bears within the specified weight range based on the ogive graph.
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Video duration:
2mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Ogive
An ogive is a cumulative frequency graph that represents the number of observations below a particular value in a dataset. It is constructed by plotting cumulative frequencies against the upper boundaries of the class intervals. This graph helps in visualizing the distribution of data and allows for easy determination of how many observations fall within a specific range.
Cumulative Frequency
Cumulative frequency is the running total of frequencies in a dataset, showing the number of observations that fall below or at a certain value. It is calculated by adding the frequency of each class interval to the sum of the frequencies of all preceding intervals. This concept is essential for understanding how data accumulates and is crucial for interpreting ogives.
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Interpreting Data Ranges
Interpreting data ranges involves analyzing specific intervals within a dataset to understand the distribution of values. In the context of the question, determining the number of black bears weighing between 158.5 and 244.5 pounds requires identifying the cumulative frequencies at these weight thresholds on the ogive. This allows for the calculation of the number of bears within that weight range by subtracting the cumulative frequencies.
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