Math Problem Statement

Transformation of marks: Given the transformation formula y = (1/5)x + 40, where x represents the examination marks before the transformation and y represents the marks after the transformation. What is the mean and variance of the transformed marks?

Solution

It seems you've uploaded an image containing a mathematical transformation formula. The content discusses the transformation of marks in terms of mean and variance, where:

  • The transformation formula is given as:
    y=15x+40y = \frac{1}{5}x + 40 Here, xx represents the examination marks before the transformation, and yy represents the marks after the transformation.

  • Mean After Transformation:
    The mean of the transformed marks yy is calculated using the linearity of expectation:
    Meany=15Meanx+40\text{Mean}_y = \frac{1}{5} \text{Mean}_x + 40

  • Variance After Transformation:
    The variance of the transformed marks yy is affected by the scaling factor, and the transformation of variance is:
    Variancey=(15)2Variancex\text{Variance}_y = \left( \frac{1}{5} \right)^2 \text{Variance}_x

Do you need help with a specific part of the transformation, or would you like to proceed with an example? Let me know if you need any further clarifications or calculations.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Transformation
Mean
Variance

Formulas

y = (1/5)x + 40
Mean_y = (1/5)Mean_x + 40
Variance_y = (1/5)^2 Variance_x

Theorems

Linearity of Expectation

Suitable Grade Level

Grades 9-12