Math Problem Statement
Find the range and standard deviation of the set of data. 4, 8, 9, 11, 13, 15
Solution
import numpy as np
Dataset
data = [4, 8, 9, 11, 13, 15]
Calculating range
data_range = max(data) - min(data)
Calculating standard deviation
std_deviation = np.std(data)
data_range, std_deviation(11, 3.559026084010437)(11, 3.559026084010437)successThe range of the dataset is 11, and the standard deviation is approximately 3.56.
Do you want a detailed explanation of how these were calculated or have any further questions?
Here are 5 related questions for practice:
- How would the range and standard deviation change if we added the value 20 to the dataset?
- Can you find the variance of this dataset?
- What is the mean (average) of this dataset?
- How do outliers affect the range and standard deviation?
- Can you compute the range and standard deviation for the dataset: 3, 6, 9, 12, 15, 18?
Tip: Standard deviation gives you an idea of how spread out the numbers are from the mean.
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Math Problem Analysis
Mathematical Concepts
Descriptive Statistics
Range
Standard Deviation
Formulas
Range = Max(data) - Min(data)
Standard Deviation (σ) = sqrt((Σ(xi - μ)^2) / N)
Theorems
Properties of Measures of Dispersion
Suitable Grade Level
Grades 9-11
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