Math Problem Statement

What is the median and mean of the data set.

What is the median and mean of the data set?

Solution

To calculate the mean and median of the data set provided in the image, I will first extract the numbers, organize them, and perform the calculations.

Extracted Data:

  • Column 1: 253, 245, 175, 162, 210, 201, 236, 189, 246, 216, 213
  • Column 2: 131, 213, 170, 188, 255, 267, 163, 241, 263, 269, 179
  • Column 3: 304, 315, 323, 317, 290, 231, 262, 253, 245, 215, 225

Combined Data Set:

253,245,175,162,210,201,236,189,246,216,213,131,213,170,188,255,267,163,241,263,269,179,304,315,323,317,290,231,262,253,245,215,225253, 245, 175, 162, 210, 201, 236, 189, 246, 216, 213, 131, 213, 170, 188, 255, 267, 163, 241, 263, 269, 179, 304, 315, 323, 317, 290, 231, 262, 253, 245, 215, 225

I will now calculate the mean and median. numpy as np

Data extracted from the image

data = [ 253, 245, 175, 162, 210, 201, 236, 189, 246, 216, 213, 131, 213, 170, 188, 255, 267, 163, 241, 263, 269, 179, 304, 315, 323, 317, 290, 231, 262, 253, 245, 215, 225 ]

Calculating the mean and median

mean_value = np.mean(data) median_value = np.median(data)

mean_value, median_value### Results:

  • Mean: 232.27 (approx.)
  • Median: 236.0

Would you like a step-by-step explanation of how these were calculated?

Here are some related questions for further exploration:

  1. How does the mean compare to the median in terms of distribution?
  2. What is the range of this data set?
  3. Can we calculate the standard deviation to analyze the data's spread?
  4. How would outliers (if present) affect the mean and median?
  5. What would the mode of the data set be?

Tip: The median is often a better measure than the mean in datasets with outliers or skewed distributions!

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Math Problem Analysis

Mathematical Concepts

Statistics
Mean
Median

Formulas

Mean = Sum of all data points / Number of data points
Median = Middle value of the ordered data set (or average of two middle values if even number of points)

Theorems

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Suitable Grade Level

Grades 9-12