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 2.5.28b
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?
Verified step by step guidance1
Step 1: Recall that a box-and-whisker plot divides the data into quartiles, with the box representing the interquartile range (IQR) and the whiskers extending to the minimum and maximum values. Identify the position of \$23.39 on the plot relative to the quartiles.
Step 2: Determine which quartile \$23.39 falls into. If it is above the third quartile (Q3), then it represents the upper 25% of the data. If it is within the IQR, calculate its position relative to Q3.
Step 3: Use the cumulative percentage of the quartiles to estimate the percentage of employees earning more than \$23.39. For example, if \$23.39 is above Q3, then the percentage of employees earning more than \$23.39 is less than 25%.
Step 4: If \$23.39 is within the IQR, calculate the proportion of the data in the upper quartile that exceeds \$23.39. This can be done by determining the relative position of \$23.39 within the range of Q3 to the maximum value.
Step 5: Combine the results from the previous steps to express the percentage of employees earning more than \$23.39 as a proportion of the total data set.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Box-and-Whisker Plot
A box-and-whisker plot is a graphical representation of a data set that displays its minimum, first quartile, median, third quartile, and maximum. It helps visualize the distribution and identify outliers. The box represents the interquartile range (IQR), while the 'whiskers' extend to the smallest and largest values within 1.5 times the IQR from the quartiles.
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Percentile
A percentile is a measure used in statistics to indicate the value below which a given percentage of observations fall. For example, the 75th percentile means that 75% of the data points are below that value. Understanding percentiles is crucial for interpreting data distributions and determining how a specific value compares to the rest of the data set.
Calculating Percentages
Calculating percentages involves determining the proportion of a part relative to the whole, expressed as a fraction of 100. In the context of the question, to find the percentage of employees earning more than a specific hourly rate, one would count the number of employees above that rate and divide by the total number of employees, then multiply by 100 to convert it to a percentage.
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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
Drawing a Box-and-Whisker Plot In Exercises 15–18,
(b) draw a box-and-whisker plot that represents the data set.
4 7 7 5 2 9 7 6 8 5 8 4 1 5 2 8 7 6 6 9
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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
Use the ogive to approximate
the height for which the cumulative frequency is 15.
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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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