Math Problem Statement

The length (in pages) of math research projects is given. Calculate the range, variance, and standard deviation for the dataset: 15, 24, 19, 22, 299, 19, 35, 31, 27.

Solution

For the given data, the following values are calculated:

  • Range: 284
  • Variance: 7504.02 (rounded to 2 decimal places)
  • Standard Deviation: 86.63 (rounded to 2 decimal places)

Would you like further details on these calculations?

Here are some related questions:

  1. How is the range of a dataset determined?
  2. What is the difference between population variance and sample variance?
  3. Why do we use the square root of variance to calculate standard deviation?
  4. How do outliers affect the standard deviation and variance?
  5. How would you compute these statistics for a different dataset?

Tip: Standard deviation provides a clearer picture of data spread compared to the variance, especially when the original unit of measurement is important.

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Math Problem Analysis

Mathematical Concepts

Statistics
Data Analysis

Formulas

Range = Max value - Min value
Variance = Σ(X - Mean)² / N
Standard Deviation = √Variance

Theorems

Measures of Spread
Variance and Standard Deviation

Suitable Grade Level

Grades 10-12

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