80, 90, 40, 30, 20, 10, 70, 60, 50
To find the difference between the two medians, we first calculate the median of the original data and then the median of the data after the replacement.
Median Calculation: Original Data
The original data set is:
80, 90, 40, 30, 20, 10, 70, 60, 50
First, arrange the data in ascending order:
10, 20, 30, 40, 50, 60, 70, 80, 90
There are $n=9$ observations. The median is the middle value, which is the $(\frac{n+1}{2})^{th}$ term.
Median position = $(\frac{9+1}{2}) = 5^{th}$ term.
The 5th term in the sorted list is 50. So, the original median is 50.
Median Calculation: Replaced Data
Now, replace the number 30 with 100 in the original data set:
80, 90, 40, 100, 20, 10, 70, 60, 50
Arrange this new data set in ascending order:
10, 20, 40, 50, 60, 70, 80, 90, 100
The number of observations is still $n=9$. The median is again the $(\frac{n+1}{2})^{th}$ term.
Median position = $(\frac{9+1}{2}) = 5^{th}$ term.
The 5th term in this sorted list is 60. So, the new median is 60.
Difference Calculation: Final Step
The question asks for the difference between the two medians.
Difference = (New Median) - (Original Median)
Difference = $60 - 50$
Difference = $10$
The difference between the two medians is 10.
Similar Questions
- 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: - 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.
$9, 35, 20, 25, 25, 15, 25$ - 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?
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.
What will be the difference between mean and median of the given data?
21, 11, 27, 8, 5, 12, 7, 23, 3, 14, 9, 19Find 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
