Math Problem Statement
Value
18
19
15
20
25
31
17
35
27
22
34
29
40
33
21 find the standard deviation
Solution
To find the standard deviation (SD) of the given data set, follow these steps:
Given values:
Step 1: Find the Mean ()
The mean is calculated as:
where represents the values and is the number of values.
Step 2: Find Each Value’s Deviation from the Mean and Square It
We'll compute these in the next step.
Step 3: Compute the Variance ()
The variance formula is:
Let's calculate this.
Step 4: Compute the Standard Deviation ()
The standard deviation is:
Now, let’s calculate the exact standard deviation. numpy as np
Given data set
data = np.array([18, 19, 15, 20, 25, 31, 17, 35, 27, 22, 34, 29, 40, 33, 21])
Compute standard deviation (population standard deviation)
std_dev = np.std(data, ddof=0) # Using population formula
std_devThe standard deviation of the given data set is approximately 7.38.
Would you like a detailed breakdown of the calculations?
Related Questions:
- What is the difference between population and sample standard deviation?
- How does standard deviation help in data analysis?
- Can standard deviation be negative? Why or why not?
- How does standard deviation relate to variance?
- What are real-life examples where standard deviation is useful?
Tip: A lower standard deviation means the data points are closer to the mean, while a higher standard deviation indicates more spread.
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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
Standard Deviation Theorem
Variance Theorem
Suitable Grade Level
Grades 9-12
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