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.
Important Questions from Measures of Central Tendency
If X̅ = 20 is the mean of 10 observations x1, x2, ... x10; then what is the value of \(\displaystyle \sum_{i=1}^{10}\left(\frac{3 x_i-4}{5}\right) ?\) ?
What is the mean of the numbers 1, 2, 3, ... 10 with frequencies 9C0, 9C1, 9C2 ..., 9C9, respectively?
Which one of the following measures of central tendency is used in construction of index numbers?
The mean of five numbers is 30. If one number is excluded, their mean becomes 28. The excluded number is
The ‘less than’ ogive curve and the ‘more than’ ogive curve intersect at
