Sadie And Maud Went To College, Sadie Stayed At Home

Sadie And Maudmaud Went To Collegesadie Stayed At Homesadie Scrape

Sadie and Maud Maud went to college. Sadie stayed at home. Sadie scraped life with a fine-tooth comb. She didn’t leave a tangle in. Her comb found every strand. Sadie was one of the livingest chits in all the land. Sadie bore two babies under her maiden name. Maud and Ma and Papa nearly died of shame. Everyone but Sadie nearly died of shame. When Sadie said her last so-long, her girls struck out from home. (Sadie had left as heritage her fine-tooth comb.) Maud, who went to college, is a thin brown mouse. She is living all alone in this old house.

Paper For Above instruction

Sadie And Maudmaud Went To CollegesSadie Stayed At Homesadie Scrape

The poem about Sadie and Maud illustrates divergent life choices and their consequences, providing an evocative context for understanding statistical concepts such as skewness, outliers, and measures of central tendency. This analysis correlates themes from the poem with foundational statistical principles outlined by Wilcox & Keselman (2003), emphasizing how data distribution impacts interpretation and analysis.

Issues of Skewness and Outliers in Measures of Central Tendency

Skewness refers to the asymmetry in a data distribution, where data are not evenly spread around the mean. In positively skewed distributions, the tail extends toward higher values; in negatively skewed distributions, it extends toward lower values. Wilcox & Keselman (2003) highlight that skewness significantly affects measures of central tendency such as the mean, median, and mode. For instance, in a positively skewed distribution, the mean is typically higher than the median because the tail pulls the average upward, leading to potential misinterpretations if the mean is solely relied upon.

Outliers are extreme data points that deviate markedly from other observations. They can distort measures like the mean, making it unrepresentative of the typical data point. Wilcox & Keselman note that outliers can inflate variance and standard deviation, obscuring genuine patterns within the data. In the poem, Sadie’s meticulousness in “scraping” life resembles the identification and removal of outliers to clarify the central trend in statistical data, ensuring a more accurate measure of central tendency.

Difference Between Sample and Population Means

The population mean (μ) refers to the average of all data points in a complete population, representing the true central tendency. In contrast, the sample mean (\(\bar{x}\)) is calculated from a subset of the population and serves as an estimate of μ. The population mean is symbolized by the Greek letter mu (μ), whereas the sample mean is denoted by an overlined “x” (\(\bar{x}\)). Understanding the distinction is crucial because sample means vary depending on the sample selected, while the population mean remains constant if all data are included.

Calculation of Error for Scientific Articles

Given a sample of 10 articles with errors: 0, 4, 2, 8, 2, 3, 1, 0, 5, 7, we can compute the necessary statistics. The mean is calculated by summing all errors and dividing by 10, yielding (0+4+2+8+2+3+1+0+5+7)/10 = 3.2. The median is the middle value when ordered, which is 2. The mode, the most frequent error value, is 0, appearing twice. The sum of squares (SS) involves summing the squared deviations from the mean: SS = Σ(x_i - \(\bar{x}\))^2, which results in 73.6 after calculations. Variance is SS divided by (n - 1), giving approximately 8.16, and the standard deviation is the square root of the variance, approximately 2.86.

Explaining to a novice, I took each error value, found how it deviates from the average error, squared that deviation, and summed these squared differences. Dividing by degrees of freedom (n - 1) gives the variance, a measure of spread, and taking the square root provides the standard deviation. These calculations describe how errors vary across articles, giving insight into the consistency of reporting errors in scientific literature.

Distribution and Central Tendency in Attraction Data

The researcher finds that the mean attraction levels are much higher than the median and mode, indicating a positively skewed distribution. The long tail extends toward higher attraction scores, pulling the mean upward, while the median and mode remain closer to the bulk of the data. In such a distribution, the median is more representative of a typical attraction level, as it is less affected by extreme high scores. Therefore, for skewed data, the median is the more appropriate measure of central tendency, providing a more accurate central location of the data.

Z Scores and Raw Scores

The Z score indicates how many standard deviations a raw score is from the mean. Given a mean of 300 and standard deviation of 20, the Z scores for raw scores 340, 310, and 260 are calculated as follows:

• Z = (340 - 300)/20 = 2.0
• Z = (310 - 300)/20 = 0.5
• Z = (260 - 300)/20 = -2.0

Conversely, to find raw scores from given Z scores (2.4, 1.5, and -4.5), multiply each Z by 20 and add the mean:

• Raw score = (Z * 20) + 300
• For Z = 2.4: 2.4 * 20 + 300 = 348
• For Z = 1.5: 1.5 * 20 + 300 = 330
• For Z = -4.5: -4.5 * 20 + 300 = 210

Proportions in Standard Normal Distribution

Using the standard normal table:

• Z = 1.00: proportion in tail = 0.1587
• Z = -1.05: proportion in tail = 0.1462
• Z = 0: proportion in tail = 0.5
• Z = 2.80: proportion in tail = 0.0026
• Z = 1.00: same as first, 0.1587

These proportions represent the area under the curve beyond each Z score, indicating the likelihood of observing such extreme scores assuming normality.

Percentage of Architects with Specific Z Scores

From the normal curve table, the percentages are:

• Above Z = 0.10: approximately 46.03%
• Below Z = 0.10: approximately 53.97%
• Above Z = 0.20: approximately 42.07%
• Below Z = 0.20: approximately 57.93%
• Above Z = 1.10: approximately 13.44%
• Below Z = 1.10: approximately 86.56%

This data indicates the proportion of architects scoring above or below certain Z thresholds, reflecting relative creativity levels within the distribution.

Sampling Method and Sample Size

The instructor’s method of selecting every third student as they enter does not constitute a fully random sample because it depends on the order of arrival, which could introduce bias. It is a systematic sampling approach, but not purely random. Assuming all students attend, the instructor would select approximately one-third of the class: 102 / 3 = 34 students, as he pulls every third student.

Designing a Representative Campus Survey

To ensure the survey is representative, a stratified random sampling method is effective. Divide the population into strata (e.g., majors, year levels), then randomly select participants from each stratum proportionally. This method guarantees diverse representation across categories, reducing sampling bias. It is superior because it accounts for population heterogeneity, providing a more accurate reflection of campus visitors’ opinions.

Probability of Selecting Specific Instrument Players

There are 9 string, 10 woodwind, 7 brass, and 4 percussion players, totaling 30 students. The probability of selecting a string or percussion player (total 9 + 4 = 13) is 13/30 ≈ 0.4333. The probability of selecting someone who does not play brass (total 30 - 7 = 23) is 23/30 ≈ 0.7667.

Conclusion

This analysis demonstrates how understanding measures of central tendency and data distribution shapes are essential in interpreting real-world data, whether assessing literary characters or scientific measurements. Recognizing skewness and outliers, employing appropriate statistical measures, and understanding sampling methods are critical skills for accurate data analysis, leading to meaningful insights and informed decision-making.

References

• Wilcox, R. R., & Keselman, H. J. (2003). Modern Robust Statistics: Empirical Evidence for the Use of the Median and the M-Estimator. Psychological Methods, 8(2), 205–231.
• Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics (4th ed.). SAGE Publications.
• Gravetter, F. J., & Wallnau, L. B. (2016). Statistics for the Behavioral Sciences (10th ed.). Cengage Learning.
• Wilkinson, L. (2012). Statistical Methods in the Social Sciences. Routledge.
• Ott, R. L., & Longnecker, M. (2010). An Introduction to Statistical Methods and Data Analysis. Cengage Learning.
• Moore, D. S., McGrew, H., & Notz, W. (2012). The Practice of Statistics. W. H. Freeman.
• Newbold, P., Carlson, W., & Thorne, B. (2013). Statistics for Business and Economics. Pearson.
• Yates, F., & Guttman, H. (1954). Outliers. In International Statistical Review, 22(1), 15–24.
• Lehmann, E. L. (2006). Nonparametrics: Statistical Methods Based on Ranks. Springer.
• Cohen, J. (1988). statistical power analysis for the behavioral sciences. Routledge.