Math Problem Statement

Weight (in Kg) of 20 students was as follows 55, 50, 46, 48, 59, 57, 65,63, 61,48, 45, 53, 67. 65, 68, 62, 60, 56, 51, 54 Calculate Mean, Median and Standard Deviation (SD) for above data

Solution

import numpy as np

Data

weights = [55, 50, 46, 48, 59, 57, 65, 63, 61, 48, 45, 53, 67, 65, 68, 62, 60, 56, 51, 54]

Calculations

mean_weight = np.mean(weights) median_weight = np.median(weights) std_dev_weight = np.std(weights, ddof=0) # Population standard deviation

mean_weight, median_weight, std_dev_weight(56.65, 56.5, 6.994819511610003)(56.65, 56.5, 6.994819511610003)successThe calculations for the given data are as follows:

  1. Mean (Average): 56.65 kg
  2. Median: 56.5 kg
  3. Standard Deviation (SD): 6.99 kg

Would you like a detailed explanation of how these were calculated, or do you have any further questions? Here are related inquiries you might consider:

  1. How do we calculate these metrics step by step?
  2. What is the difference between population and sample standard deviation?
  3. Can you explain the significance of the median in this dataset?
  4. How do outliers affect mean, median, and standard deviation?
  5. Could we visualize this data with a histogram or box plot?

Tip: Use standard deviation to understand how data points are spread out around the mean—it’s a measure of variability!

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Math Problem Analysis

Mathematical Concepts

Statistics
Measures of Central Tendency
Measures of Spread

Formulas

Mean: sum of all values / number of values
Median: middle value in sorted data
Standard Deviation (Population): sqrt(sum((x_i - mean)^2) / N)

Theorems

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Suitable Grade Level

Grades 9-12