Calculating Mode Using Empirical Relation
This question requires calculating the mode of a dataset using the empirical relation between mean, median, and mode.
Empirical Relation Formula
The empirical relation connecting the mean, median, and mode for moderately skewed distributions is given by:
$Mode = 3 \times Median - 2 \times Mean$
Given Data
- Mean = 47
- Median = 61
Calculation Steps
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Substitute values: Plug the given mean and median values into the empirical relation formula.
$Mode = 3 \times (61) - 2 \times (47)$
-
Perform Multiplication: Calculate the products separately.
$3 \times 61 = 183$
$2 \times 47 = 94$
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Perform Subtraction: Subtract the result of the mean term from the result of the median term.
$Mode = 183 - 94$
$Mode = 89$
Result
The calculated mode of the data is 89.
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