Math Problem Statement
Find the standard deviation for 2 , 17 , 12 , 5 , 7 , 10 , 5 , 8 , 6
Solution
To calculate the standard deviation for the data set , follow these steps:
1. Find the mean:
The mean is the sum of all numbers divided by the number of data points.
2. Find the squared differences from the mean:
For each number in the data set, subtract the mean and square the result.
3. Find the average of the squared differences:
4. Take the square root of the variance to find the standard deviation:
Conclusion:
The standard deviation is approximately .
Do you need further details or have any questions?
Here are 5 related questions:
- What is the difference between standard deviation and variance?
- How does changing a single value affect the standard deviation?
- What is the significance of a low standard deviation versus a high one?
- How would you calculate the standard deviation of a larger dataset?
- Can you calculate standard deviation using other measures of central tendency?
Tip: Standard deviation gives a measure of how spread out the numbers in your data set are from the mean.
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Math Problem Analysis
Mathematical Concepts
Statistics
Standard Deviation
Mean
Variance
Formulas
Mean: μ = (Σx) / N
Variance: σ² = Σ((x - μ)²) / N
Standard Deviation: σ = √σ²
Theorems
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Suitable Grade Level
Grades 9-12
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