Math Problem Statement
Solution
The problem asks to compute the sample standard deviation of the data sample: , rounded to two decimal places.
Step-by-step solution:
Step 1: Calculate the sample mean.
The formula for the sample mean is: Where is the number of data points.
For the data :
Step 2: Calculate the squared deviations from the mean.
Next, subtract the mean from each data point and square the result:
Step 3: Calculate the sample variance.
The formula for sample variance is: Substituting the values:
Step 4: Calculate the sample standard deviation.
The sample standard deviation is the square root of the sample variance:
Final Answer:
The sample standard deviation is approximately 3.52 (rounded to two decimal places).
Would you like further details or have any questions?
Here are five related questions to consider:
- How is the sample standard deviation different from population standard deviation?
- What is the significance of using in the sample variance formula?
- How would the standard deviation change if we added an additional data point to this sample?
- What is the relationship between variance and standard deviation?
- How does standard deviation help in understanding the spread of data?
Tip: Remember that standard deviation helps quantify how much data points in a sample deviate from the mean. The larger the standard deviation, the more spread out the data.
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Math Problem Analysis
Mathematical Concepts
Statistics
Standard Deviation
Sample Mean
Variance
Formulas
Sample mean: \( \bar{x} = \frac{\sum x_i}{n} \)
Sample variance: \( s^2 = \frac{\sum (x_i - \bar{x})^2}{n - 1} \)
Sample standard deviation: \( s = \sqrt{s^2} \)
Theorems
Sample standard deviation formula
Suitable Grade Level
Grades 9-12
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