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.1a

Chapter 3, Problem 3.r.1a

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,

Verified step by step guidance

Step 1: Calculate the differences between the reported heights and measured heights for each individual. For each pair of values, subtract the measured height from the reported height. For example, for the first pair, the difference is 68.0 - 67.9 = 0.1.

Step 2: List all the calculated differences. These differences will be used to compute the mean, median, and mode.

Step 3: To find the mean, sum all the differences and divide by the total number of differences. Use the formula: \( \text{Mean} = \frac{\text{Sum of differences}}{\text{Number of differences}} \).

Step 4: To find the median, arrange the differences in ascending order and identify the middle value. If there is an even number of differences, take the average of the two middle values.

Step 5: To find the mode, identify the difference value(s) that appear most frequently in the list. If no value repeats, there is no mode.

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Key Concepts

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

Mean

The mean is the average of a set of values, calculated by summing all the values and dividing by the number of values. In this context, it will be used to find the average difference between reported and measured heights, providing insight into the overall tendency of self-reported heights compared to actual measurements.

Median

The median is the middle value in a sorted list of numbers. If the list has an even number of observations, the median is the average of the two middle numbers. This measure is particularly useful in this scenario as it helps to understand the central tendency of the differences without being affected by extreme values.

Mode

The mode is the value that appears most frequently in a data set. In the context of the height differences, identifying the mode can reveal the most common discrepancy between reported and measured heights, which can be important for understanding patterns in self-reporting accuracy.

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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

Variance of Roller Coaster Speeds The standard deviation of the sample values in Exercise 1 is 43.1 km/h. What is the variance (including units)?

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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 (h) Q1, (i) Q3

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Textbook Question

Estimating s The sample of 92 roller coaster maximum speeds includes values ranging from a low of 10 km/h to a high of 194 km/h. Use the range rule of thumb to estimate the standard deviation.

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Textbook Question

Outliers Identify any of the differences found from Exercise 1 that appear to be outliers. For any outliers, how much of an effect do they have on the mean, median, and standard deviation?

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