Math Problem Statement

67, 88, 95, 76, 56, 40, 99, 93, 48, 87, 77, 59, 100, 65, 83, 79, 61, 92, 89, 90, 54, 73, 84, 80, 60, 96, 89, 76, 54, 60, 65, 88, 85, 77, 82, 43, 75, 70, 69, 80, 50, 78, 80, 81, 79, 61, 80, 86, 90, 49, 87, 40, 90, 89, 76, 75 Find mean, median and mode

Solution

numpy as np from scipy import stats

Data

data = [ 67, 88, 95, 76, 56, 40, 99, 93, 48, 87, 77, 59, 100, 65, 83, 79, 61, 92, 89, 90, 54, 73, 84, 80, 60, 96, 89, 76, 54, 60, 65, 88, 85, 77, 82, 43, 75, 70, 69, 80, 50, 78, 80, 81, 79, 61, 80, 86, 90, 49, 87, 40, 90, 89, 76, 75 ]

Calculations

mean = np.mean(data) median = np.median(data) mode = stats.mode(data)

mean, median, mode.mode[0]The statistical measures for the given data are as follows:

  • Mean: 74.91 (approximately)
  • Median: 78.5
  • Mode: 80

Do you want a detailed explanation or further assistance? Here are related questions for deeper exploration:

  1. How can the mode be used in analyzing frequency distributions?
  2. What is the difference between mean, median, and mode in terms of data representation?
  3. How do outliers affect the mean and median differently?
  4. What is the significance of the mode when there are multiple modes?
  5. How would removing a value from this dataset affect the mean, median, and mode?

Tip: Always visualize your data using a histogram or boxplot to better understand the distribution and spot outliers.

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Math Problem Analysis

Mathematical Concepts

Statistics
Descriptive Statistics
Measures of Central Tendency

Formulas

Mean = Sum of all data points / Number of data points
Median = Middle value of the ordered dataset
Mode = Most frequently occurring value in the dataset

Theorems

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Suitable Grade Level

Grades 6-8