Math Problem Statement

[ MD = \left|0 - \frac{25}{3}\right| = \frac{25}{3} \approx 8.33 ]

Solution

The equation you've provided represents the calculation of the mean deviation (MD), but let's break it down step by step.

Given:

MD=0253MD = \left|0 - \frac{25}{3}\right|

  1. Subtraction inside the absolute value: 0253=2530 - \frac{25}{3} = -\frac{25}{3}

  2. Taking the absolute value: 253=253\left| -\frac{25}{3} \right| = \frac{25}{3}

So, the exact value of the mean deviation is:

MD=2538.33MD = \frac{25}{3} \approx 8.33

Let me know if you'd like further details, or have any questions.

Here are 5 related questions to expand on this:

  1. What is the difference between mean deviation and standard deviation?
  2. How is the mean deviation formula derived?
  3. In what situations would you prefer using mean deviation over other measures of dispersion?
  4. How does the mean deviation change if the reference value (e.g., 0 here) changes?
  5. Can you explain how absolute values affect measures of dispersion like mean deviation?

Tip: The absolute value function ensures that deviations from the mean are always positive, which prevents negative values from canceling out positive ones in deviation calculations.

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Math Problem Analysis

Mathematical Concepts

Mean Deviation
Absolute Value
Basic Algebra

Formulas

MD = \left| x_i - \mu \right|
Absolute Value: |a|

Theorems

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Suitable Grade Level

Grades 9-11