The mean of a dataset is mu, the median is M, and the mode is m, which follow the empirical formula m = 3M - 2mu (empirical relationship). Each data point x undergoes a linear transformation given by x prime = kx + d, where k and d are constants. The new mean of the transformed dataset is mu prime, the median is M prime and the mode is m prime. Which of the following options correctly represents mu prime, M prime and m prime and ensures that the empirical relationship remains valid?

Subject: Mathematics | Topic: Statistics | Difficulty: MEDIUM

Options

1. (A) mu prime = k mu + d, M prime = kM, m prime = km + d
2. (B) mu prime = k mu + d, M prime = kM + d, m prime = k(m + d)
3. (C) mu prime = k mu, M prime = kM + d, m prime = km + d
4. (D) mu prime = k mu + d, M prime = kM + d, m prime = km + d

Verified Answer

Option (D): mu prime = k mu + d, M prime = kM + d, m prime = km + d

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