Textbook Question
Using and Interpreting Concepts
Using and Interpreting Concepts Finding Quartiles, Interquartile Range, and Outliers In Exercises 11 and 12,
(b) find the interquartile range
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Ch. 2 - Descriptive Statistics
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470
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Table of contents
- Ch. 1 - Introduction to Statistics87
- Ch. 2 - Descriptive Statistics176
- Ch. 3 - Probability184
- Ch. 4 - Discrete Probability Distributions102
- Ch. 5 - Normal Probability Distributions183
- Ch. 6 - Confidence Intervals154
- Ch. 7 - Hypothesis Testing with One Sample165
- Ch. 8 - Hypothesis Testing with Two Samples134
- Ch. 9 - Correlation and Regression87
- Ch. 10 - Chi-Square Tests and the F-Distribution87
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
Chapter 2, Problem 2.1.28b
Use the ogive to approximate
the height for which the cumulative frequency is 15.
Verified step by step guidance1
Step 1: Understand the ogive graph. An ogive is a cumulative frequency graph that shows the cumulative frequency of data points up to a certain value. The x-axis represents the height (in inches), and the y-axis represents the cumulative frequency.
Step 2: Locate the cumulative frequency of 15 on the y-axis. This is the target value for which we need to approximate the corresponding height.
Step 3: Draw a horizontal line from the cumulative frequency value of 15 on the y-axis until it intersects the ogive curve.
Step 4: From the point of intersection, draw a vertical line down to the x-axis. This will give the approximate height corresponding to the cumulative frequency of 15.
Step 5: Read the value on the x-axis where the vertical line meets it. This is the approximate height for which the cumulative frequency is 15.
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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 graphical representation of cumulative frequency. It is constructed by plotting the cumulative frequency against the upper boundaries of the class intervals. The resulting curve helps visualize how many observations fall below a particular value, making it easier to determine percentiles and other statistical measures.
Cumulative Frequency
Cumulative frequency is the running total of frequencies up to a certain point in a dataset. It shows the number of observations that fall below or at a specific value. This concept is crucial for understanding distributions and is often used in conjunction with ogives to analyze data trends and percentiles.
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Creating Frequency Polygons
Interpolation
Interpolation is a statistical method used to estimate unknown values that fall within the range of a discrete set of known data points. In the context of the ogive, interpolation allows us to approximate the height corresponding to a specific cumulative frequency, such as 15, by finding the point on the curve that aligns with that frequency.
Related Practice
Textbook Question
Drawing a Box-and-Whisker Plot In Exercises 15–18,
(b) draw a box-and-whisker plot that represents the data set.
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Textbook Question
Hourly Earnings Refer to the data set in Exercise 26 and the box-and-whisker plot you drew that represents the data set.
b. What percent of the employees made more than \$23.39 per hour?
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Textbook Question
Mean Absolute Deviation Another useful measure of variation for a data set is the mean absolute deviation (MAD). It is calculated by the formula
MAD = Σ |x − x̄| / n.
b. Find the mean absolute deviation of the data set in Exercise 16. Compare your result with the sample standard deviation obtained in Exercise 16.
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Textbook Question
Extending Concepts
Trimmed Mean To find the 10% trimmed mean of a data set, order the data, delete the lowest 10% of the entries and the highest 10% of the entries, and find the mean of the remaining entries.
b. Compare the four measures of central tendency, including the midrange.
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Textbook Question
What Would You Do? You work at a bank and are asked to recommend the amount of cash to put in an ATM each day. You do not want to put in too much (which would cause security concerns) or too little (which may create customer irritation). The daily withdrawals (in hundreds of dollars) for 30 days are listed. 72 84 61 76 104 76 86 92 80 88 98 76 97 82 84 67 70 81 82 89 74 73 86 81 85 78 82 80 91 83
If you put \$9000 in the ATM each day, what percent of the days in a month should you expect to run out of cash? Explain.
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