Calculating Mode using Empirical Relation
The problem asks for the mode of a data set given its mean and median.
Given Data:
- Mean ($ \bar{x} $) = 20
- Median (M) = 30
Empirical Relation:
For a moderately skewed distribution, the empirical relationship between mean, median, and mode is given by:
Mode $ = 3 \times \text{Median} - 2 \times \text{Mean} $
Or, using notation:
Mode $ = 3M - 2\bar{x} $
Calculation:
Substitute the given values into the formula:
Mode $ = (3 \times 30) - (2 \times 20) $
Mode $ = 90 - 40 $
Mode $ = 50 $
Result:
The mode of the data is 50.
Important Questions from Elementary Statistics
What is the mode of the given data?
3, 0, 1, 0, 2, 1, 2, 0, 1, 2, 1, 1, 1, 3, 2What is the mode of the given data?
21, 22, 23, 23, 24, 21, 22, 23, 21, 23, 24, 23, 21, 23A bowler has taken 0, 3, 2, 1, 5, 3, 4, 5, 5, 2, 2, 0, 0, 1 and 2 wickets in 15 consecutive matches. What is the mode of the given data?
The data given below shows the number of people who have saved a certain amount of money.
Saving (In Rs.)
Number of people
5
1
15
3
20
4
25
2
30
1
35
1
40
2
What is the median of the given data?
If the ratio of mean and median of a certain data is 4 : 5, then find the ratio of its mean and mode.
