Math Problem Statement

Compute the mean, range, and standard deviation for the heights of the recruits. Round to the nearest tenth if necessary.

Solution

PIL import Image import pytesseract

Load the image

image_path = '/mnt/data/1733282637502ra3qbzan.jpg' image = Image.open(image_path)

Perform OCR to extract text

extracted_text = pytesseract.image_to_string(image) extracted_textThe text extraction is partially unclear, but here's the cleaned-up content:

The heights of nine army recruits (first list) and nine randomly-selected people walking through a mall (second list) are given. The question asks to compute the mean, range, and standard deviation for the heights of the recruits, rounding to the nearest tenth.

Heights of the recruits (List 1): 80, 75, 67, 70, 68, 69, 72, 71, 70
Heights of people in the mall (List 2): 34, 79, 56, 52, 72, 63, 69, 44, 65

Let me calculate the required statistics for List 1 (army recruits). numpy as np

Heights of the recruits

recruits_heights = np.array([80, 75, 67, 70, 68, 69, 72, 71, 70])

Calculations for the recruits

mean_recruits = np.mean(recruits_heights) range_recruits = np.ptp(recruits_heights) # Range is max - min std_dev_recruits = np.std(recruits_heights, ddof=0) # Standard deviation

mean_recruits, range_recruits, std_dev_recruitsFor the heights of the recruits:

  • The mean height is approximately 71.3 inches.
  • The range of the heights is 13 inches.
  • The standard deviation is approximately 3.8 inches.

Would you like similar calculations for the second list (mall heights) or further breakdowns? Here are five related questions for further learning:

  1. How are mean, median, and mode related in data analysis?
  2. Why is standard deviation a useful measure of data spread?
  3. How would the statistics change if one extreme outlier were added to the list?
  4. How do you calculate variance from the standard deviation?
  5. Can you apply these statistics to real-world applications, such as height predictions?

Tip: Always double-check your data input to ensure accuracy in your calculations.

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Math Problem Analysis

Mathematical Concepts

Mean
Range
Standard Deviation
Descriptive Statistics

Formulas

Mean = (Sum of all data points) / (Number of data points)
Range = Maximum value - Minimum value
Standard Deviation = sqrt((Σ (xᵢ - μ)²) / N)

Theorems

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Suitable Grade Level

Grades 9-12