Calculating Mean Using Median and Mode Relationship
The problem asks us to find the mean of a dataset given its median and a relationship between the mean and the mode.
Given Information
- The mean of the data is four times the mode: Mean = 4 * Mode.
- The median of the data is 63.
Applying the Empirical Relationship
For a distribution that is moderately skewed, we can use the empirical relationship between the mean, median, and mode:
\(Mean - Mode = 3 * (Mean - Median)\)
Step-by-Step Calculation
- Let M represent the Mean, Mo represent the Mode, and Md represent the Median.
- We are given:
- M = 4 * Mo
- Md = 63
- From M = 4 * Mo, we can express the Mode in terms of the Mean: Mo = M / 4.
- Now, substitute the known values and the expression for Mo into the empirical formula:
\(M - (M / 4) = 3 * (M - 63)\)
- Simplify the equation:
\((4M - M) / 4 = 3M - 189\)
\(3M / 4 = 3M - 189\)
- To eliminate the fraction, multiply both sides by 4:
\(3M = 4 * (3M - 189)\)
\(3M = 12M - 756\)
- Rearrange the terms to solve for M:
\(756 = 12M - 3M\)
\(756 = 9M\)
- Calculate the Mean:
\(M = 756 / 9\)
\(M = 84\)
Conclusion
The calculated mean of the data is 84.
Similar Questions
- What is the mode of the following data?
44, 45, 51, 50, 53, 54, 46, 40, 51, 46, 40, 42, 55, 42, 44, 55, 49, 44 - The marks obtained by 9 students of a class in mathematics are 76, 85, 47, 67, 85, 76, 47, 76, 67. What is the mode of these numbers?
- What is the mode of the following data?
89, 76, 76, 88, 81, 81, 65, 90, 83, 89, 64, 63, 78, 64, 82, 87, 79, 89, 87, 65, 86, 77, 80, 70, 67 - What is the mode of the following data?
86, 84, 71, 82, 82, 63, 84, 71, 70, 86, 88, 65, 71, 81, 87, 60, 60, 74, 78, 62, 75, 66, 68, 85, 72 - What is the mode of the following data?
89, 89, 64, 86, 64, 79, 81, 85, 82, 81, 75, 85, 82, 84, 61, 82, 81, 64, 74, 71, 61, 68, 77, 64, 79 - What is the mode of the following data?
55, 50, 48, 43, 55, 41, 54, 51, 41, 45, 53, 54, 52, 41, 49, 54, 41, 49 - What is the mode of the following data?
70, 70, 73, 71, 74, 69, 80, 68, 66, 66, 89, 83, 81, 86, 82, 74, 86, 87, 67, 72, 62, 76, 86, 65, 62 - What is the mode of the following data?
78, 60, 85, 76, 84, 86, 73, 89, 78, 77, 60, 63, 62, 72, 61, 78, 67, 77, 61, 78, 75, 61, 88, 66, 69 - What is the mode of the following data?
70, 79, 66, 89, 68, 80, 82, 80, 71, 84, 69, 68, 61, 85, 71, 84, 68, 86, 73, 75, 83, 88, 64, 88, 65 - What is the mode of the following data?
48, 42, 46, 42, 44, 43, 48, 49, 48, 45, 53, 46, 47, 47, 49, 53, 50, 41
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.
