Math Problem Statement

Calculate the standard deviation and variance of the sample data shown, to two decimal places

x

27.6

1.2

29.4

12

26

Standard deviation: 

Variance: 

Solution

The variance of the sample data is 149.17 and the standard deviation is 12.21.

Would you like further details or have any questions?

Here are some related questions to consider:

  1. How do you interpret the standard deviation and variance in this context?
  2. What is the difference between sample variance and population variance?
  3. How would the values change if you added an outlier to the dataset?
  4. What does a low standard deviation indicate about a dataset?
  5. How is variance used in different statistical methods?

Tip: Remember that the variance is the square of the standard deviation, which means they represent the same information but on different scales.

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Math Problem Analysis

Mathematical Concepts

Statistics
Variance
Standard Deviation
Sample Data

Formulas

Variance formula: σ² = Σ(xi - x̄)² / (n - 1)
Standard Deviation formula: σ = √Variance

Theorems

The concept of variance and its relationship with standard deviation

Suitable Grade Level

Grades 10-12