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
-
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
A random sample of 20 people is classified in the following table according to their ages:
Age
Frequency
15 – 25
2
25 – 35
4
35 – 45
6
45 – 55
5
55 - 65
3
What is the mean age of this group of people?
The median of the following observations 46, 64, 87, 41, 58, 77, 35, 90, 55, 92, 33 is 58. If 92 is replaced by 99 and 41 by 43 in the above data. The new median is:
If the difference of mode and median is 36, then the difference of median and mean is:
In a Mathematics test 15 students scored 80 marks, 20 students scored 75 marks, 28 students scored 65 marks and 25 students scored 60 marks, mode of the score is:
If the mode of the scores 10, 12, 13, 15, 15, 13, 12, 10, x is 15, then what is the value of x?
