Median Salary Calculation
The median is the middle value in a dataset ordered by magnitude. For 100 employees, the median falls between the 50th and 51st values when salaries are sorted.
Salary Distribution Analysis
Let's determine the salary range for the 50th and 51st employees:
- Employees 1-45: Earn Rs. 20,000
- Employees 46-70: Earn Rs. 30,000 (Cumulative count: 45 + 25 = 70)
- Employees 71-90: Earn Rs. 40,000 (Cumulative count: 70 + 20 = 90)
- Employees 91-98: Earn Rs. 60,000 (Cumulative count: 90 + 8 = 98)
- Employees 99-100: Earn Rs. 150,000 (Cumulative count: 98 + 2 = 100)
Determining the Median Salary
Both the 50th and 51st employees fall within the group earning Rs. 30,000. Therefore:
- Salary of the 50th employee = Rs. 30,000
- Salary of the 51st employee = Rs. 30,000
The median is the average of these two middle salaries:
Median = $ \frac{\text{Rs. } 30,000 + \text{Rs. } 30,000}{2} $
Median = $ \frac{\text{Rs. } 60,000}{2} $
Median = Rs. 30,000
Important Questions from Mean Median Mode
- Five integers are picked from 0 to 20, with possible repetitions, such that their mean is 12, median is 18, and they have a single mode of 20.
Ignoring permutations, the number of ways to pick these five integers is _____ A data set is given to be $[1, 2, 0, -1, -3, 1, 2, 0, 1]$.
The median of the data set is ____. (rounded off to the nearest integer)
- The following sequence of numbers is arranged in increasing order: 1, x, x, x, y, y, 9,16,18. Given that the mean and median are equal, and are also equal to twice the mode, the value of y is
- The sample average of 50 data points is 40. The updated sample average after including a new data point taking the value of 142 is ________.
The mean absolute deviation about the median for the data 3, 9, 5, 3, 12, 10, 18, 4, 7, 19, 21 (rounded off to two decimal places) is ________________.
