Ch. 3 - Describing, Exploring, and Comparing Data

Triola - Elementary Statistics 14th Edition

Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook

Triola 14th Edition

Ch. 3 - Describing, Exploring, and Comparing Data

Problem 3.r.1h

Chapter 3, Problem 3.r.1h

Reported and Measured Heights Listed below are self-reported heights of males aged 16 and over and their corresponding measured heights (based on data from the National Health and Nutrition Examination Survey). All heights are in inches. First find the differences (reported height–measured height), and then use those differences to find the (h) Q1, (i) Q3

Verified step by step guidance

Step 1: Calculate the differences between the reported heights and the measured heights for each individual. Use the formula: Difference = Reported Height - Measured Height. For example, for the first individual, the difference is 68.0 - 67.9 = 0.1.

Step 2: List all the calculated differences in a new dataset. For example, the differences for the given data will be a list of values corresponding to each pair of reported and measured heights.

Step 3: Arrange the differences in ascending order. This step is necessary to calculate the quartiles (Q1 and Q3).

Step 4: Identify Q1 (the first quartile) by finding the value at the 25th percentile of the ordered differences. If the dataset size is not a multiple of 4, interpolate between the nearest ranks.

Step 5: Identify Q3 (the third quartile) by finding the value at the 75th percentile of the ordered differences. Again, interpolate if necessary to determine the exact value.

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Key Concepts

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

Differences Calculation

To analyze the self-reported and measured heights, one must first calculate the differences between the reported and measured values. This is done by subtracting the measured height from the reported height for each individual. These differences will help in understanding the accuracy of self-reported data and are essential for further statistical analysis.

Quartiles

Quartiles are statistical measures that divide a dataset into four equal parts, providing insights into the distribution of data. The first quartile (Q1) represents the 25th percentile, while the third quartile (Q3) represents the 75th percentile. Calculating Q1 and Q3 from the differences will help identify the spread and central tendency of the discrepancies between reported and measured heights.

Data Interpretation

Data interpretation involves analyzing the calculated differences and quartiles to draw conclusions about the self-reported heights. Understanding how these differences vary can reveal patterns, such as whether individuals tend to overestimate or underestimate their heights. This analysis is crucial for assessing the reliability of self-reported data in health surveys.

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Textbook Question

Estimating Standard Deviation Listed below are sorted weights (g) of a sample of M&M plain candies randomly selected from one bag. Use the range rule of thumb to estimate the value of the standard deviation of all 345 M&Ms in the bag. Compare the result to the standard deviation of 0.0366 g computed from all of the 345 M&Ms in the bag.

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Textbook Question

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Textbook Question

Reported and Measured Heights Listed below are self-reported heights of males aged 16 and over and their corresponding measured heights (based on data from the National Health and Nutrition Examination Survey). All heights are in inches. First find the differences (reported height–measured height), and then use those differences to find the (a) mean, (b) median, (c) mode,

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Textbook Question

Roller Coaster z Score A larger sample of 92 roller coaster maximum speeds has a mean of 85.9 km/h and a standard deviation of 28.7 km/h. What is the z score for a speed of 34 km/h? Does the z score suggest that the speed of 34 km/h is significantly low?

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Textbook Question

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Textbook Question

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