Chpt 3 Project Ella Tucker

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Davidson County Community College *

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152

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Statistics

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Apr 3, 2024

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Chapter 3 Project Results – Type Names of Group Members Here Directions: For this project, we compared the weather for two cities around the globe using measures of central tendency, measures of dispersion, and measures of position. Now we want to interpret our results. Be sure to answer each question in a complete sentence or paragraph depending on the nature of the question. 1. Fill in the table below with your results from StatCrunch. Round to two decimal places. If your StatCrunch results say multiple modes, you will need to find each mode to record in the table below. Statistic: Shenyang, China Doha, Qatar Mean 51.686207 80.493103 Variance 69.931946 13.208522 Standard Deviation 8.3625323 3.6343531 Median 50.9 81.4 Range 32.5 14.6 Min 37.6 72.2 Max 70.1 86.8 Q1 45.5 79 Q3 56.6 82.6 IQR 11.1 3.6 Mode 46.2 Multiple Modes 2. Which city, on average (by average here we mean the “mean”), had a higher temperature? Explain your answer using your StatCrunch results. Doha, Qatar had a higher average temperature than Shenyang, China. Doha had an average temperature of around 80.5 while Shenyang had an average temperature of around 51.7. 3. What is the mode for Shenyang, China? Explain what it means. The mode for Shenyang, China is 46.2. This means that 46.2 is the most common number in the data set. 4. What is the mode for Doha, Qatar? Explain what it means. The city Doha, Qatar has multiple modes. This means that it has multiple numbers that appear the most throughout the data.

5. It was 60.1°F in Shenyang, China and 71.7°F in Doha, Qatar on April 15, 2020. We want to compare the two temperatures relative to their data from the previous year. We need to find z-scores in order to do that. We want to find out in which city it was cooler relative to their temperatures from April 2019. Use the rounded values in your calculations. a. Compute the z-score for Shenyang, China. 60.1-51.69=8.41 z-score for Shenyang, China = 1.01 8.41/8.36=1.006 b. Compute the z-score for Doha, Qatar. 71.7 - 80.49=-8.79 z-score for Doha, Qatar = -2.42 -8.79/3.63=-2.421 c. Which city was it relatively cooler in on April 15, 2020 based on your results from above? Doha, Qatar is relatively cooler because 71.7 degrees is less than the average temperature by 2.42 standard deviations. 6. Which city has more dispersion based on standard deviation? Explain your answer using your StatCrunch results. Shenyang, China has more dispersion because its standard deviation is larger than Doha, Qatar. 7. Which city has more dispersion based on range? Explain your answer using your StatCrunch results. Based on range, Shenyang has more dispersion because the range is larger than Doha. 8. Which city has more dispersion based on IQR? Explain your answer using your StatCrunch results. Based on IQR, Shenyang, China has more dispersion because the IQR is larger than Doha, Qatar. 9. Which measure of dispersion is used for symmetric data? Refer to your class notes . Standard deviation is used for symmetric data. 10. Which measure of dispersion is used for skewed data? Refer to your class notes. IQR is used for skewed data. 11. Based on the mean and median results, describe the approximate shape of the distribution for Shenyang, China . Explain your answer using your StatCrunch results. Construct a histogram to check this as well. Plot the mean and median on the histogram. Paste your graph below. The approximate shape of the distribution for Shenyang, China is skewed right because the mean is greater than the median.

12. Thinking back to your answer to the previous question: Based on the approximate shape of this distribution, answer the questions below: a. Which measure is the best to use when describing the center of the data from Shenyang, China? Median is best to use when describing the center of the data from Shenyang. b. Which measure is the best to use when describing the spread of the data from Shenyang, China? IQR is best to use when describing the spread of the data from Shenyang. 13. Based on the mean and median results, describe the approximate shape of the distribution for Doha, Qatar. Explain your answer using your StatCrunch results. Construct a histogram to check this as well. Plot the mean and median on the histogram. Paste your graph below. The approximate shape of the distribution for Doha, Qatar is skewed left because the mean is less than the median.

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14. Thinking back to your answer to the previous question: Based on the approximate shape of this distribution, answer the questions below: a. Which measure is the best to use when describing the center of the data from Doha, Qatar? Median is best to use when describing the center of the data from Doha, Qatar. b. Which measure is the best to use when describing the spread of the data from Doha, Qatar? IQR is best to use when describing the spread of the data from Doha, Qatar. 15. Are the shapes of the distributions for your two selected cities the same? No, the shapes of the distributions are not the same. One is skewed to the left and one is skewed to the right. 16. Review your answers to questions 6 through 15. Answer the following questions: a. Can you compare the two sets of data? Yes, you can compare the two sets of data. b. Based on the measure of dispersion for the type of data (refer back to questions 11 and 14), which city has more dispersion if you can compare the two sets of data? Explain your answer using your StatCrunch results. Shenyang, China has more dispersion than Doha, Qatar because its IQR is larger.

17. State the five-number summary for Shenyang. 37.6, 45.5, 50.9, 56.6, 70.1 18. Calculate the lower and upper fences for Shenyang. 1.5 * 11.1=16.65 The upper fence for Shenyang is 72.65. 56 + 16.65=72.65 1.5 * 11.1=16.65 The lower fence for Shenyang is 28.35. 45.5 - 16.65=28.35 19. Are there any outliers for Shenyang? If so, what are they? Explain how you knew this. No, there is no observation lower than 28.5 (the lower fence) or greater than 72.65 (the upper fence). 20. Construct a boxplot for Shenyang. Paste your graph below. Be sure to make it horizontal. 21. State the five-number summary for Doha. 74.4, 79, 81.4, 82.6, 86.8 22. Calculate the lower and upper fences for Doha. 1.5 * 3.6 =5.4 The upper fence for Doha is 87.6. 82.2 + 5.4= 87.6 1.5 * 3.6=5.4 The lower fence for Doha is 73.6. 79 - 5.4= 73.6 23. Are there any outliers for Doha? If so, what are they? Explain how you knew this. Yes, there is an observation greater than 73.6.

24. Construct a boxplot for Doha. Paste your graph below. Be sure to make it horizontal.

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Chpt 3 Project Ella Tucker

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