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Here is a histogram and summary statistics of the average monthly Internet cost (in dollars) in 576 cities worldwide: Summary statistics: # of Cities 150 100+ 50 61 n 576 37.56 191 30 Mean Std. dev. 22.93 145 132 200+ # of Cities 150 i) According to the Normal model, in what percentage of the 576 cities should the average monthly Internet cost be more than one standard deviation below the mean? 100 29 ii) From the histogram, in what percentage of the 576 cities actually is the average monthly Internet cost more than one standard deviation below the mean? 50 21 60 90 120 150 180 210 Average Internet Monthly Cost iii) What characteristic of the histogram might explain the discrepancy between parts i) and ii). iv) In an attempt to work with a more symmetric distribution, your study partner decided to plot the histogram for the In transformed data. They plotted the following histogram showing the middle ~68% of the Indata. Median Range Min Max Q₁ Q3 34.14 231.87 1.49 233.36 23.51 49.35 16.1% 1 240 67.9% In(Internet) 3.98 16% They also calculated some summary statistics and obtained that the mean Indata is 3.46 with standard deviation 0.62. Can you show them that the Normal model still does not apply to the transform data?

Here is a histogram and summary statistics of the average monthly Internet cost (in dollars) in 576 cities worldwide: Summary statistics: # of Cities 150 100+ 50 61 n 576 37.56 191 30 Mean Std. dev. 22.93 145 132 200+ # of Cities 150 i) According to the Normal model, in what percentage of the 576 cities should the average monthly Internet cost be more than one standard deviation below the mean? 100 29 ii) From the histogram, in what percentage of the 576 cities actually is the average monthly Internet cost more than one standard deviation below the mean? 50 21 60 90 120 150 180 210 Average Internet Monthly Cost iii) What characteristic of the histogram might explain the discrepancy between parts i) and ii). iv) In an attempt to work with a more symmetric distribution, your study partner decided to plot the histogram for the In transformed data. They plotted the following histogram showing the middle ~68% of the Indata. Median Range Min Max Q₁ Q3 34.14 231.87 1.49 233.36 23.51 49.35 16.1% 1 240 67.9% In(Internet) 3.98 16% They also calculated some summary statistics and obtained that the mean Indata is 3.46 with standard deviation 0.62. Can you show them that the Normal model still does not apply to the transform data?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Here is a histogram and summary statistics of the average monthly Internet cost (in dollars) in 576 cities worldwide: ### Histogram The histogram displays the distribution of average monthly Internet costs among the cities: - The x-axis represents the average Internet monthly cost in dollars, ranging from 0 to 240. - The y-axis shows the number of cities. - Most cities (191) have costs between $0 and $30. - There is a significant decrease in the number of cities as the cost increases, with 145 cities in the $30-$60 range, and very few cities above $90. ### Summary Statistics - **n:** 576 - **Mean:** \$37.56 - **Standard Deviation:** \$22.93 - **Median:** \$34.14 - **Range:** \$231.87 - **Minimum:** \$1.49 - **Maximum:** \$233.36 - **Q1 (First Quartile):** \$23.51 - **Q3 (Third Quartile):** \$49.35 ### Questions i) According to the Normal model, in what percentage of the 576 cities should the average monthly Internet cost be more than one standard deviation below the mean? ii) From the histogram, in what percentage of the 576 cities is the average monthly Internet cost actually more than one standard deviation below the mean? iii) What characteristic of the histogram might explain the discrepancy between parts i) and ii)? iv) In an attempt to work with a more symmetric distribution, your study partner decided to plot the histogram for the ln-transformed data. They plotted the following histogram showing the middle ~68% of the ln-data. ### ln(Internet) Histogram This histogram represents the natural logarithm of Internet costs: - The distribution appears more symmetric compared to the original data. - The central portion indicates that 67.9% of cities fall within a logged cost range, with 16.1% on either side of this central range. Summary statistics for ln-transformed data show a mean of 3.46 with a standard deviation of 0.62. The Normal model still does not apply well to this transformed data.
Transcribed Image Text:Here is a histogram and summary statistics of the average monthly Internet cost (in dollars) in 576 cities worldwide: ### Histogram The histogram displays the distribution of average monthly Internet costs among the cities: - The x-axis represents the average Internet monthly cost in dollars, ranging from 0 to 240. - The y-axis shows the number of cities. - Most cities (191) have costs between $0 and $30. - There is a significant decrease in the number of cities as the cost increases, with 145 cities in the $30-$60 range, and very few cities above $90. ### Summary Statistics - **n:** 576 - **Mean:** \$37.56 - **Standard Deviation:** \$22.93 - **Median:** \$34.14 - **Range:** \$231.87 - **Minimum:** \$1.49 - **Maximum:** \$233.36 - **Q1 (First Quartile):** \$23.51 - **Q3 (Third Quartile):** \$49.35 ### Questions i) According to the Normal model, in what percentage of the 576 cities should the average monthly Internet cost be more than one standard deviation below the mean? ii) From the histogram, in what percentage of the 576 cities is the average monthly Internet cost actually more than one standard deviation below the mean? iii) What characteristic of the histogram might explain the discrepancy between parts i) and ii)? iv) In an attempt to work with a more symmetric distribution, your study partner decided to plot the histogram for the ln-transformed data. They plotted the following histogram showing the middle ~68% of the ln-data. ### ln(Internet) Histogram This histogram represents the natural logarithm of Internet costs: - The distribution appears more symmetric compared to the original data. - The central portion indicates that 67.9% of cities fall within a logged cost range, with 16.1% on either side of this central range. Summary statistics for ln-transformed data show a mean of 3.46 with a standard deviation of 0.62. The Normal model still does not apply well to this transformed data.
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