Math Problem Statement

from my data set [3,8,7,10,4,24,3,12,7,2,6,5,4,1,6,5,14,3,17,1,24,14,2,16,4,2,5,5,3,8,12,15] I want to know if my histogram is positively or negatively skwewd

Solution

import numpy as np import matplotlib.pyplot as plt from scipy.stats import skew

Dataset

data = [3, 8, 7, 10, 4, 24, 3, 12, 7, 2, 6, 5, 4, 1, 6, 5, 14, 3, 17, 1, 24, 14, 2, 16, 4, 2, 5, 5, 3, 8, 12, 15]

Calculate skewness

data_skewness = skew(data)

Plot histogram

plt.hist(data, bins=10, edgecolor='black', alpha=0.7) plt.title('Histogram of Dataset') plt.xlabel('Value') plt.ylabel('Frequency') plt.axvline(np.mean(data), color='red', linestyle='dashed', linewidth=1, label='Mean') plt.axvline(np.median(data), color='blue', linestyle='dashed', linewidth=1, label='Median') plt.legend() plt.show()

data_skewness <<ImageDisplayed>>1.1571430605262341.157143060526234successThe skewness of the dataset is approximately 1.16, which indicates a positive skew. This means that the right tail of the histogram is longer or that there are more extreme values on the higher end of the data distribution.

Would you like further analysis or details on this? Here are 5 follow-up questions you might consider:

  1. Would you like to see the specific numerical values of the mean, median, and mode of the dataset?
  2. Should we test the normality of this data using statistical tests (e.g., Shapiro-Wilk)?
  3. Do you need help identifying how the skewness might impact analysis or interpretation of this dataset?
  4. Would you like to visualize the boxplot for a clearer representation of the data distribution and outliers?
  5. Should we transform the data (e.g., logarithmic or square root) to reduce skewness for further analysis?

Tip: A positive skew often suggests the presence of outliers on the higher end; analyzing these points individually can provide additional insights.

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Math Problem Analysis

Mathematical Concepts

Statistics
Skewness
Data Visualization
Histogram Analysis

Formulas

Skewness formula: Skewness = (3 * (Mean - Median)) / Standard Deviation

Theorems

Measures of Central Tendency
Properties of Skewness in Distributions

Suitable Grade Level

Grades 9-12