Math Problem Statement

The length (in pages) of math research projects is given below. Using this information, calculate the range, variance, and standard deviation. 10, 30, 19, 36, 25, 299, 16, 16, 22 The lack of what property of the standard deviation accounts for its sensitivity to the one data value that is significantly larger than the others?

Solution

From the provided data, the following results are calculated:

  • Range = 289
  • Variance = 7646.69
  • Standard Deviation = 87.45

Regarding the question on standard deviation's sensitivity, the correct answer is:

  • B. Resistance: Standard deviation is sensitive to outliers because it lacks resistance, meaning it is easily affected by extreme values like the "299" in the data.

Do you need more details or have any questions? Here are some related questions:

  1. How is the range of a data set different from the interquartile range?
  2. What effect does an outlier like "299" have on the mean and standard deviation?
  3. How would you interpret the standard deviation in this context?
  4. Can standard deviation ever be negative?
  5. What is the difference between population variance and sample variance?

Tip: Outliers can disproportionately affect measures like variance and standard deviation, so it's crucial to examine them carefully.

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Math Problem Analysis

Mathematical Concepts

Descriptive Statistics
Measures of Dispersion
Range
Variance
Standard Deviation

Formulas

Range = max(data) - min(data)
Variance = Σ(xi - μ)^2 / N
Standard Deviation = sqrt(Variance)

Theorems

Measures of dispersion theory
Impact of outliers on standard deviation

Suitable Grade Level

Grade 9-12

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