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
- 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:
- Which of the following CANNOT take a negative value?
- The given data is arranged in ascending order and its median is 17. Find the value of $x$.
$8, 10, 12, 15, x, x + 2, 20, 25, 30, 32$ - Find the sum of the mean, median and mode of the given data.
$9, 35, 20, 25, 25, 15, 25$ - 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 - A alone can complete a work in 12 days and B alone can complete the same work in 18 days. They started working together, but A left after 3 days. In how many days will B alone be able to complete the remaining work?
- For the data set 1, 2, 3, 5, 2, 3, 4, 6, 6, 8, 3, 4, 5 which of the following options is INCORRECT?
Important Questions from Elementary Statistics
In a colony 5 families have 1 child, 7 families have 2 children, 8 families have 3 children and 3 families have 4 children.What is the mode of the number of children.
Find the mode and median of 3, 4, 5, 5, 3, 6, 7, 3, 5, 5, 6.
A. 5 and 5
B. 3 and 5
C. 5 and 4
D. 3 and 4
For which set of numbers do the mean, median and mode all have the same value?
The median of 5, 8, 25, 22, 34, 18 is
Find the mean of first 5 two-digit multiples of 4.
