Table of contents

1. Intro to Stats and Collecting Data55m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically1h 45m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables2h 33m
6. Normal Distribution and Continuous Random Variables1h 38m
7. Sampling Distributions & Confidence Intervals: Mean1h 53m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample2h 19m
10. Hypothesis Testing for Two Samples3h 22m
11. Correlation1h 6m
12. Regression1h 4m
13. Chi-Square Tests & Goodness of Fit1h 20m
14. ANOVA1h 0m

2. Describing Data with Tables and Graphs

Frequency Distributions

Statistics

2. Describing Data with Tables and Graphs

Frequency Distributions

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2:00 minutes

Problem 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 guidance

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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Key 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.

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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use the ogive to approximate

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In Exercises 17–19, use the data set, which represents the points recorded by each player on the Winnipeg Jets in the 2019–2020 NHL season. (Source: National Hockey League)

8 8 8 6 0 73 26 1

0 5 58 1 7 5 10 63

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Textbook Question

Construct a frequency distribution for the data set using the indicated number of classes. In the table, include the midpoints, relative frequencies, and cumulative frequencies. Which class has the greatest class frequency and which has the least class frequency.

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Textbook Question

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Use the ogive to approximate thethe number of black bears that weigh between 158.5 pounds and 244.5 pounds.

Key Concepts

Ogive

Cumulative Frequency

Interpreting Data Ranges

Watch next

Use the ogive to approximate the
the number of black bears that weigh between 158.5 pounds and 244.5 pounds.