Difference Calculation: Mean vs Median Using Mode
Statistics often uses relationships between measures of central tendency. For data that is moderately skewed, an empirical relationship exists between the mean, median, and mode.
Understanding the Empirical Relationship
The common empirical relationship for unimodal and moderately skewed distributions is stated as:
$Mean$ - $Mode$ = 3 \times ($Mean$ - $Median$)
Applying the Formula
We are given that the difference between the mean and the mode is 69.
- Given: $\text{Mean} - \text{Mode} = 69$
Substitute this value into the empirical formula:
$69 = 3 \times (\text{Mean} - \text{Median})$
Solving for Mean-Median Difference
To find the difference between the mean and the median, rearrange the equation:
- Divide both sides by 3: $ \frac{69}{3} = \text{Mean} - \text{Median} $
- Calculate the result: $ 23 = \text{Mean} - \text{Median} $
Therefore, the difference between the mean and the median is 23.
Similar Questions
- 40 % is the passing criteria in an examination. Out of 9 students who appeared, 4 failed and the remaining received 80 %, 55 %, 52 %, 66 % and 81% marks. The median of the percentage marks is equal to:
- Find the median and the mode of the following data:
2, 3, 5, 7, 2, 3, 3, 5, 7 and 9. - The following observations are arranged in ascending order. If the median of the data is 19, then find the value of x.
6, 9, 15, x + 4, x + 8, x + 12, 30, 32 - The marks scored by 10 students are given below.
17, 19, 12, 20, 19, 14, 15, 18, 19, 14
The mode of the given data is: - The marks scored by 10 students are given below.
18, 13, 14, 14, 19, 14, 17, 17, 14, 20
The mode of the data is: - In the given data if 30 is replaced by 100 then find the difference of the two medians.
80, 90, 40, 30, 20, 10, 70, 60, 50 - Find the mean height of persons from the following data.
Height (cm) Number of persons 120 3 130 4 140 5 150 6 160 2 - If the mean of the following data is k, then find the value of k.
Value 3 2 k 4 5 Frequency k 2k 3k 4k 5k - Let a set S = {1, 2, 2, 3, 3, 3, 4, 4, 4, 4}. Then the value of $4 \times \text{mean} + 2 \times \text{mode} - 8 \times \text{median}$ is:
- The weights (in kg) of 7 men are 64, 63, 62, 65, 67, 66 and 61. The median weight is:
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.
