Math Problem Statement
Find the standard deviation for the group of data items. 11, 11, 14, 14, 14, 14
Solution
To calculate the standard deviation of the given data set:
Data: 11, 11, 14, 14, 14, 14
Steps:
-
Find the Mean (μ):
-
Find the squared deviations from the mean:
- For 11:
- For 11:
- For 14:
- For 14:
- For 14:
- For 14:
-
Sum of the squared deviations:
-
Variance (σ²): Since this is a sample, use the formula for sample variance:
-
Standard Deviation (σ):
So, the standard deviation is approximately 1.55.
Would you like more details or have any other questions?
Related questions:
- How do you calculate the variance from raw data?
- What is the difference between sample and population standard deviation?
- Can you explain how to find the mean for a larger data set?
- What is the importance of standard deviation in data analysis?
- How do outliers affect the standard deviation?
Tip: The standard deviation measures how spread out the data is around the mean.
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Math Problem Analysis
Mathematical Concepts
Statistics
Mean
Variance
Standard Deviation
Formulas
Mean (μ) = Σx_i / n
Variance (σ²) = Σ(x_i - μ)² / (n - 1) (for sample data)
Standard Deviation (σ) = √(Variance)
Theorems
Sample Variance and Standard Deviation
Suitable Grade Level
Grades 10-12
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