Questions: Math 1200 - Fall 2024 Exam 1 Extra Credit - 52 points Please show all of your work. Do not just write the answers. Explain how you found your answers. Go to https://dcmpdatatools.utdanacenter.org/edaquantitative/ In the Choose Dataset menu, select Youth Unemployment Rate in EU. You should get the descriptive statistics and histogram as shown below. This data set contains the youth unemployment rates in European Union countries from 2023. For example, in one country, the youth unemployment rate was 14.2%. 1. Describe the center, shape, and spread of the distribution. (15 points) 2. Which measure of center, mean or median, best describes the typical data value in the distribution? Why? (5 points) 3. Interpret the IQR. What does this tell you about the distribution? (4 points) 4. Discuss the presence of outliers in the distribution. Use the IQR Rule to justify whether the distribution has outliers. Show the calculation of the lower fence and upper fence for outliers. (10 points) 5. Interpret the standard deviation of the distribution. What does this tell you about the variation in the distribution? (4 points) 6. Based on the Empirical Rule: (10 points) (a) What interval captures the middle 68% of values in the distribution? (b) What interval captures the middle 95% of values in the distribution? (f) What interval captures the middle 99.7% of values in the distribution?

Math 1200 - Fall 2024 Exam 1 Extra Credit - 52 points Please show all of your work. Do not just write the answers. Explain how you found your answers. Go to https://dcmpdatatools.utdanacenter.org/edaquantitative/ In the Choose Dataset menu, select Youth Unemployment Rate in EU. You should get the descriptive statistics and histogram as shown below. This data set contains the youth unemployment rates in European Union countries from 2023. For example, in one country, the youth unemployment rate was 14.2%. 1. Describe the center, shape, and spread of the distribution. (15 points) 2. Which measure of center, mean or median, best describes the typical data value in the distribution? Why? (5 points) 3. Interpret the IQR. What does this tell you about the distribution? (4 points) 4. Discuss the presence of outliers in the distribution. Use the IQR Rule to justify whether the distribution has outliers. Show the calculation of the lower fence and upper fence for outliers. (10 points) 5. Interpret the standard deviation of the distribution. What does this tell you about the variation in the distribution? (4 points) 6. Based on the Empirical Rule: (10 points) (a) What interval captures the middle 68% of values in the distribution? (b) What interval captures the middle 95% of values in the distribution? (f) What interval captures the middle 99.7% of values in the distribution?
Transcript text: Math 1200 - Fall 2024 Exam 1 Extra Credit - 52 points Please show all of your work. Do not just write the answers. Explain how you found you answers. Go to https://dcmpdatatools.utdanacenter.org/eda_quantitative/ In the Choose Dataset menu, select Youth Unemployment Rate in EU. You should get the descriptive statistics and histogram as shown below. This data set contains the youth unemployment rates in European Union countries from 2023. For example, in one country, the youth unemployment rate was $14.2 \%$. 1. Describe the center, shape, and spread of the distribution. (15 points) 2. Which measure of center, mean or median, best describes the typical data value in the distribution? Why? (5 points) 3. Interpret the IQR. What does this tell you about the distribution? (4 points) 4. Discuss the presence of outliers in the distribution. Use the IQR Rule to justify whether the distribution has outliers. Show the calculation of the lower fence and upper fence for outliers. (10 points) 5. Interpret the standard deviation of the distribution. What does this tell you about the variation in the distribution? (4 points) 6. Based on the Empirical Rule: (10 points) (a) What interval captures the middle $68 \%$ of values in the distribution? (b) What interval captures the middle $95 \%$ of values in the distribution? (f) What interval captures the middle $99.7 \%$ of values in the distribution?
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Solution

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Solution Steps

Step 1: Describe the center, shape, and spread of the distribution
  • Center: The mean of the distribution is 11.1, and the median is 10.1. These values indicate the central tendency of the data.
  • Shape: The histogram shows a distribution that appears to be slightly right-skewed, as there are more values clustered on the left side and a few higher values on the right.
  • Spread: The standard deviation is 5.58, indicating the average distance of the data points from the mean. The range (difference between the maximum and minimum values) is 23.4 (27.3 - 4.9). The interquartile range (IQR) is 5.9, which measures the spread of the middle 50% of the data.
Step 2: Which measure of center, mean or median, best describes the typical data value in the distribution? Why?
  • Median: The median (10.1) is a better measure of the typical data value in this distribution because the data is slightly right-skewed. The mean (11.1) is affected by the higher values on the right, which can distort the central tendency. The median is more robust to outliers and skewed data.
Step 3: Interpret the IQR. What does this tell you about the distribution?
  • IQR Interpretation: The IQR is 5.9, which is the range of the middle 50% of the data. This indicates that the middle half of the youth unemployment rates in the EU countries varies by 5.9 percentage points. A smaller IQR would indicate that the data points are closer to the median, while a larger IQR indicates more variability within the middle 50% of the data.

Final Answer

  1. The center of the distribution is around 11.1 (mean) and 10.1 (median), the shape is slightly right-skewed, and the spread is indicated by a standard deviation of 5.58 and an IQR of 5.9.
  2. The median best describes the typical data value because it is less affected by the skewness and outliers in the distribution.
  3. The IQR of 5.9 tells us that the middle 50% of the youth unemployment rates vary by 5.9 percentage points, indicating moderate variability within this range.
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