Math Problem Statement
Find the SD of the given data set - 7, 2, 8, 11, 6, 13, 16
Solution
To calculate the standard deviation (SD) of a given data set, follow these steps:
Data Set:
7, 2, 8, 11, 6, 13, 16
Step 1: Find the Mean (Average)
The formula for the mean is:
where represents each value in the data set, and is the number of data points.
Step 2: Find the Squared Differences from the Mean
For each data point, subtract the mean and then square the result.
Step 3: Find the Variance
The variance is the average of these squared differences. The formula for variance is:
Step 4: Find the Standard Deviation
The standard deviation is the square root of the variance:
Conclusion:
The standard deviation of the data set is approximately 4.34.
Do you want more details or have any questions about the process?
Here are 5 related questions:
- How does the standard deviation change if the dataset values increase by 5 each?
- What is the variance of the data set?
- How do outliers in a data set affect the standard deviation?
- Can you explain the difference between sample standard deviation and population standard deviation?
- How would removing the largest number from the data set affect the standard deviation?
Tip: Standard deviation provides insight into how much data points deviate from the mean, with a larger SD indicating more spread in the data.
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Math Problem Analysis
Mathematical Concepts
Statistics
Standard Deviation
Variance
Formulas
Mean (μ) = (Σx_i) / n
Variance (σ^2) = Σ(x_i - μ)^2 / n
Standard Deviation (σ) = √σ^2
Theorems
None specifically required for basic SD calculation
Suitable Grade Level
Grades 9-12
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