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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1:38 minutes

Problem 2.1.6

Textbook Question

What is the difference between a frequency polygon and an ogive?

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A frequency polygon is a graphical representation of the distribution of a dataset. It is created by plotting points that represent the frequencies of data intervals and connecting these points with straight lines. The x-axis represents the midpoints of the intervals, and the y-axis represents the frequencies.

An ogive, on the other hand, is a cumulative frequency graph. It is constructed by plotting points that represent the cumulative frequencies of data intervals and connecting these points with straight lines. The x-axis represents the upper boundaries of the intervals, and the y-axis represents the cumulative frequencies.

The key difference between the two is that a frequency polygon shows the frequency of individual intervals, while an ogive shows the cumulative frequency, which accumulates as you move across intervals.

Frequency polygons are useful for comparing distributions and visualizing the shape of the data, while ogives are helpful for understanding cumulative trends and determining percentiles or medians.

Both graphs are constructed using similar principles, but they serve different purposes in statistical analysis and data visualization.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Frequency Polygon

A frequency polygon is a graphical representation of a frequency distribution. It is created by plotting the midpoints of each class interval on the x-axis and the corresponding frequencies on the y-axis, then connecting these points with straight lines. This type of graph helps visualize the shape of the distribution and is particularly useful for comparing multiple distributions.

Ogive

An ogive is a cumulative frequency graph that represents the cumulative frequency of data points up to a certain value. It is constructed by plotting the upper boundaries of class intervals on the x-axis and the cumulative frequencies on the y-axis, connecting the points with a line. Ogives are useful for determining percentiles and understanding the distribution of data over time or categories.

Cumulative Frequency

Cumulative frequency is the running total of frequencies through the classes in a frequency distribution. It indicates the number of observations that fall below a particular value or within a certain range. Understanding cumulative frequency is essential for constructing ogives, as it allows for the visualization of how data accumulates across intervals, providing insights into the overall distribution.

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Related Practice

Textbook Question

In Exercises 1–5, use the data listed in the margin, which are magnitudes (Richter scale) and depths (km) of earthquakes from Data Set 24 “Earthquakes” in Appendix B

Frequency Distribution Construct a frequency distribution of the magnitudes. Use a class width of 0.50 and use a starting value of 1.00.

Textbook Question

In Exercises 1–5, use the data listed in the margin, which are magnitudes (Richter scale) and depths (km) of earthquakes from Data Set 24 “Earthquakes” in Appendix B

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Frequency Distribution For the frequency distribution from Exercise 1, find the following.

a. Class limits of the first class

b. Class boundaries of the first class

c. Class midpoint of the first class

Textbook Question

Hershey Kisses Refer to Data Set 38 “Candies” and use the weights (grams) of Hershey’s Kisses. Begin with a lower class limit of 4.300 g and use a class width of 0.100 g. Does this distribution appear to be a normal distribution?

Textbook Question

Testing Goodness-of-Fit with a Normal Distribution Refer to Data Set 1 “Body Data” in Appendix B for the heights of females.

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a. Enter the observed frequencies in the table above.

Textbook Question

use the frequency distribution to find the (a) class width, (b) class midpoints, and (c) class boundaries.

Toledo, OH, Average Normal Temperatures (F)

Textbook Question

use the ogive to approximate

the number in the sample.

Textbook Question

Use the ogive to approximate