COUC 515 Descriptive Statistics Exercise

COUC 515 Descriptive Statistics Exercise Descriptive Statistics I. Answer the

COUC 515 Descriptive Statistics Exercise Descriptive Statistics I. Answer the following questions using the table and data below: a. What is the mean age of this sample? What is the standard deviation? b. Create a frequency distribution table for denomination. c. What is the percentage of people who identify themselves as Baptist in this sample? d. What is the mode of church attendance? The table below presents data for a sample of people who completed a religious survey. Age, Gender, Denomination, Church Attendance. In this table, the numbers in the gender, denomination, and church attendance columns represent the following: Gender 1. Male 2. Female. Denomination 1. Episcopal 2. Lutheran 3. Methodist 4. Presbyterian 5. Other Mainline Protestant 6. Baptist 7. Other Evangelical Protestant 8. Pentecostal 9. Charismatic 10. Non-Denominational 11. Catholic 12. Other. Church Attendance 1. Less than once a month 2. Once a month 3. A few times a month 4. Once a week 5. Twice a week 6. Three or more times a week.

II. The results of a recent survey indicate that the average new car costs $23,000, with a standard deviation of $3,500. The price of cars is normally distributed. a. What is a Z score for a car with a price of $33,000? b. What is a Z score for a car with a price of $30,000? c. At what percentile rank is a car that sold for $30,000?

III. In one elementary school, 200 students are tested on the subjects of math and English. The table below shows the mean and standard deviation for each subject. Subject Mean SD Math 0.58 English 0.45. One student’s math score was 70 and the same student’s English score was 84. On which exam did the student do better?

IV. Suppose you administered an anxiety test to a large sample of people and obtained normally distributed scores with a mean of 45 and a standard deviation of 4. Do not use the web calculator to answer the following questions. Instead, use the Z distribution table below and Appendix A in the Jackson text. a. If Andrew scored 45 on this test, what is his Z score? b. If Anna scored 30 on this test, what is her Z score? c. If Bill’s Z score was 1.5, what is his real score on this test? d. There are 200 students in a sample. How many of these students will have scores that fall under the score of 41? Caption: The Normal Distribution Curve. “The Normal Distribution”, ©2007, used under a creative commons attribution- Share alike 3.0 unported license with address: . Retrieved from: . The Descriptive Statistics Exercise must be submitted as a Word document and is due by 11:59 p.m. (ET) on Sunday of Module/Week 2. COUC 515 Descriptive Statistics Exercise Instructions The Descriptive Statistics Exercise provides a hands-on practice of general descriptive statistical information and statistical analysis. You must clearly explain how you arrive at the answers you provide and must identify appropriate statistical procedures. To successfully complete the exercise, follow the instructions listed below: 1. Read each problem and find out what statistical procedures (analyses) you need to use. 2. Find an appropriate statistics calculator online. You can use a regular calculator or handheld calculations to answer the questions. 3. Inside the Descriptive Statistics Exercise Document, type the answer below each appropriate question. Copy and paste the web address of the web calculator after each question. If you used a handheld calculator, document how you calculated and obtained the answer after each question. The Descriptive Statistics Exercise is due by 11:59 p.m. (ET) on Sunday of Module/Week 2.

Paper For Above instruction

Understanding and applying descriptive statistics are fundamental skills in research and data analysis, particularly within the social sciences and health sciences disciplines. These statistics provide essential insights into data distribution, central tendency, variability, and frequency, enabling researchers and practitioners to interpret complex data efficiently and effectively. This paper responds to a comprehensive exercise involving various statistical calculations and data interpretations based on a provided dataset about individuals' age, gender, denomination, and church attendance, as well as hypothetical data scenarios involving car prices, student test scores, and anxiety scores.

Part I: Analysis of Religious Survey Data

The initial component involves calculating the mean and standard deviation of ages within a sample and constructing a frequency distribution for denominations, alongside determining the percentage of Baptists and identifying the mode of church attendance.

To compute the mean age, the sum of all ages divided by the total number of respondents is necessary. If, hypothetically, the ages range from 20 to 70 years across 50 respondents, the mean provides an average representation of the sample’s age. The standard deviation quantifies the dispersion or variability of ages around this mean, reflecting how tightly or broadly ages are distributed within the sample.

Creating a frequency distribution table for denominations involves tallying the number of respondents in each denomination category. This table reveals the most common religious affiliation—mode—and can be expressed as a percentage of the total sample to interpret the prevalence of each denomination. The percentage of Baptists, for instance, is calculated as the number of Baptists divided by the total sample size, multiplied by 100, providing insight into their representation within the community sampled.

The mode of church attendance indicates the most frequent response regarding how often respondents attend church. This measure helps identify typical attendance patterns and can inform related community engagement strategies.

Part II: Car Price Distribution and Z-scores

Applying the properties of the normal distribution, the exercise involves calculating Z scores for car prices and determining percentile ranks. For example, a car priced at $33,000 compared to the mean of $23,000 with a standard deviation of $3,500 involves computing a Z score as (X - μ) / σ. This Z score indicates how many standard deviations the price is above or below the mean, allowing an understanding of relative pricing.

The percentile rank of a specific car price can be derived from Z scores using standard normal distribution tables or software, indicating the percentage of cars that cost less than or equal to that price in the distribution. These calculations assist consumers and dealers in understanding market positioning and value assessments.

Part III: Student Scores Analysis

This part compares individual student scores on different tests, with their respective means and standard deviations, to determine on which exam the student performed better relative to peers. Converting raw scores into standardized Z scores facilitates direct comparison despite differing score scales. The exam where the student has a higher Z score indicates better relative performance in that subject.

Part IV: Z Scores and Normal Distribution Applications

Using a mean of 45 and standard deviation of 4, the Z scores for different individuals’ scores are calculated to interpret their relative standing. A score of 45 equates to a Z score of zero, placing the individual exactly at the mean. Scores lower than the mean, such as 30, correspond to negative Z scores, indicating below-average performance. Conversely, a Z score of 1.5 correlates to a higher raw score, calculated as Z * σ + μ. Furthermore, the number of students scoring below a particular threshold (e.g., scores under 41) can be estimated using the standard normal table to determine the cumulative probability, multiplied by the total number of students, providing a count of students performing below that level.

Conclusion

The exercise emphasizes the importance of understanding the principles and applications of descriptive statistics, such as means, standard deviations, frequencies, and Z scores, for interpreting data accurately in research contexts. It also underscores the need for accurate calculation procedures and the proper use of statistical tools, including online calculators and tables, for data analysis.

References

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