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
- 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: - 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:
- Find the sum of the mean and median of the given data.
12, 10, 16, 18, 20, 26, 14, 28
Important Questions from Elementary Statistics
Demand for seats in a university is at its highest in the fall; demand also trends to grow and fall off in 25 year waves. In time service forecasting, the former demand characteristic would be called ______ and the latter would be called _______.
The system of combining two or more overlapping series of index numbers to obtain a single continuous series is called
The rise in the number of patients due to heatstroke is an example of:
According to government data, 24 percent of teenagers in India under the age of 18 years live in households with incomes that are classified at a particular income level. A simple random sample of 400 teenagers in India under the age of 18 years was selected for a study of learning. If the government data is correct, which of the following best approximates the probability that at least 27 per cent of the teenagers in the sample live in households that are classified at a particular income level?
Which index satisfies the factor reversal test?
