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.
$3 \times 61 = 183$
$2 \times 47 = 94$
-
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
What is mean deviation about the median ?
The mode and median of a data is 26.7 and 71, respectively. What is the mean of the data? (Use empirical formula.)
Study the given table and answer the question that follows. The given table depicts the percentage of marks scored by Mary and Perul in History and Physics (out of 75 each).
Name History Physics Mary
60
64
Perul
54
70
How many marks did Mary score in History?
The average of eight numbers is 14. The average of six of these numbers is 16. The average of the remaining two numbers is:
The value of
(1 + cot²θ)(1 + cosθ)(1 - cosθ) - (1 - sinθ)(1 + sinθ)(1 + tan²θ) is: (θ lies in the first quadrant)
