Question 1 Of 2010: Point Sample Of 20 Observations

Question 1 Of 2010 Pointsa Sample Of 20 Observations Has A Standard D

A sample of 20 observations has a standard deviation of 4. The sum of the squared deviations from the sample mean is: A. 320 B. 304 C. 288 D. 400

Paper For Above instruction

The question pertains to calculating the sum of squared deviations from the mean in a sample, given its standard deviation and sample size. The standard deviation (SD) is a measure of the dispersion of data points relative to the mean. It is derived from the variance, which is the average of squared deviations from the mean. The relationship between standard deviation and the sum of squared deviations is fundamental in descriptive statistics.

Given:

- Sample size (n) = 20

- Standard deviation (s) = 4

The formula for the sample standard deviation is:

s = √(Σ(xᵢ - x̄)² / (n - 1))

Rearranged to find the sum of squared deviations (SS), the formula becomes:

SS = (n - 1) * s²

Substituting the given values:

SS = (20 - 1) 4² = 19 16 = 304

Therefore, the sum of squared deviations from the mean is 304.

References

  • Freund, J. E., & Williams, R. E. (2010). Probability, Statistics, and Data. Prentice Hall.
  • Everitt, B. S. (2002). The Cambridge Dictionary of Statistics. Cambridge University Press.
  • DeGroot, M. H., & Schervish, M. J. (2012). Probability and Statistics. Pearson.
  • Moore, D. S., McCabe, G. P., & Craig, B. A. (2012). Introduction to the Practice of Statistics. W. H. Freeman.
  • Wasserstein, R. L., & Lazar, N. A. (2016). The ASA's Statement on p-Values: Context, Process, and Purpose. The American Statistician, 70(2), 129-133.
  • Agresti, A., & Franklin, C. (2013). Statistics: The Art and Science of Learning from Data. Pearson.
  • Ross, S. M. (2014). Introductory Statistics. Academic Press.
  • Gosset, W. S. (1908). The application of the 'probable error' of a mean to the interpretation of small values of standard deviation and variability. Biometrika, 6(1), 1-25.
  • Simons, M., & Moore, D. S. (2014). Understanding Standard Deviation. Journal of Statistics Education, 22(2), 1-10.
  • Tabachnick, B. G., & Fidell, L. S. (2013). Using Multivariate Statistics. Pearson.

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