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:

  1. How would the range and standard deviation change if we added the value 20 to the dataset?
  2. Can you find the variance of this dataset?
  3. What is the mean (average) of this dataset?
  4. How do outliers affect the range and standard deviation?
  5. 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