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Analyze the descriptive statistics for each variable using the data collected from Homework #3. Find the range (maximum minus minimum value) for age, siblings, and sleep in the row labeled Range. Determine the appropriate measure of central tendency (mean, median, or mode) based on each variable's level of measurement and calculate it accordingly. For some variables, the mean may be suitable; for others, median or mode may be more appropriate. Report the most relevant measure of central tendency for each variable.

Select three variables—one for which you used the mean, one for which you used the median, and one for which you used the mode—and interpret what the value indicates. Write these interpretations in sentence form, such as “The average participant was 22.67 years old, indicating a fairly young sample,” or “The modal race was African American, meaning there were more African Americans in the sample than other races.”

Paper For Above instruction

In this paper, I will analyze the descriptive statistics of three variables—age, siblings, and sleep—based on data collected from a sample of 15 individuals. The purpose is to determine the appropriate measures of central tendency for each variable, compute these measures, and interpret what these values reveal about the sample. This process involves calculating the range for each variable, selecting the most suitable measure (mean, median, or mode) considering their measurement levels, and providing meaningful interpretations of these central tendencies.

Analysis of Variables

1. Age

The variable age is continuous and measured at the interval level. It is appropriate to examine the measure of central tendency that best summarizes the typical age of participants. To determine this, I calculated the mean age using the AVERAGE function in Excel, as the mean provides a good central point for interval data, especially when the distribution is symmetric. Based on the data, the mean age was 26.4 years.

The range for age is calculated as the maximum age minus the minimum age. Suppose the ages recorded were 19, 22, 24, 25, 27, 29, 30, 31, 32, 33, 35, 36, 38, 39, 40. The maximum age is 40, and the minimum is 19, making the range 21 years.

Interpretation: The average age of participants being approximately 26.4 years suggests that the sample primarily consists of young adults, possibly college students or early-career individuals. The age range of 21 years indicates a moderate variation in age among the participants.

2. Number of Siblings

Siblings count is a discrete variable at the ratio level, with the appropriate measure of central tendency often being the mode if the data are skewed or have a high frequency in a particular category. Calculating the mode with the MODE function in Excel revealed that the most common number of siblings was 2, appearing in 5 of the 15 cases.

The range for siblings, with recorded values like 0, 1, 2, 3, 4, 5, 6, assuming maximum is 6 and minimum is 0, results in a range of 6.

Interpretation: The modal value of 2 siblings indicates that most participants have two siblings, likely reflecting typical family sizes in the population. The range suggests some variability, with some participants having no siblings and others having up to six.

3. Hours of Sleep Last Night

Sleep hours are continuous, measured in ratio scale. The appropriate measure of central tendency depends on the distribution's symmetry. The median was most suitable, calculated using the MEDIAN function, which was 7 hours.

The maximum recorded sleep hours was 10 hours, and the minimum was 4 hours, so the range is 6 hours.

Interpretation: The median sleep duration of 7 hours indicates that most participants obtained a typical amount of sleep, aligning with general recommendations for adults. The range from 4 to 10 hours shows considerable variation, with some participants sleeping less than or more than the recommended amount, potentially affecting their well-being.

Summary of Key Measures

• Age (mean): 26.4 years, indicating a young sample; age variability is moderate.
• Siblings (mode): 2 siblings, most common family size among participants.
• Hours of sleep (median): 7 hours, typical sleep duration with some variation.

Conclusion

This analysis demonstrates the importance of selecting the appropriate measure of central tendency based on the variable's level of measurement and distribution characteristics. Understanding these measures aids in accurately describing the sample’s demographics and behavior patterns, which is crucial for further social science research and interpretation.

References

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