Math Problem Statement
Observation 4,8,11,17,20,24,32 find standard deviation
Solution
To find the standard deviation of the data set , we will follow these steps:
Step 1: Calculate the Mean
The mean (average) of the data set is calculated as:
Where:
- are the observations,
- is the number of observations.
Step 2: Calculate Each Deviation from the Mean
Subtract the mean from each observation:
Step 3: Square Each Deviation
Square each of the deviations:
Step 4: Calculate the Variance
The variance is the mean of the squared deviations:
Step 5: Calculate the Standard Deviation
The standard deviation is the square root of the variance:
So, the standard deviation of the data set is approximately 9.00.
Would you like further details or have any questions?
Here are 5 related questions to explore further:
- How does standard deviation help in understanding data distribution?
- What is the difference between variance and standard deviation?
- How do you calculate the standard deviation for a larger data set?
- How would removing an outlier affect the standard deviation of a data set?
- What is the significance of a low versus high standard deviation in a data set?
Tip: The standard deviation is a measure of the amount of variation or dispersion in a set of values. A lower standard deviation indicates that the values tend to be close to the mean, while a higher standard deviation indicates a wider range of values.
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Math Problem Analysis
Mathematical Concepts
Statistics
Descriptive Statistics
Standard Deviation
Formulas
Mean
Variance
Standard Deviation
Theorems
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Suitable Grade Level
Grades 11-12
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