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
- The median of the following set of numbers: 154, 130, 144, 137, 156, 146, 138, 149, 160, 138 is:
- Let $X$ be a continuous random variable whose cumulative distribution function (CDF)
$F_X(x) = \begin{cases} 0 & x < t \\ \frac{x-t}{4-t} & t \le x \le 4 \\ 1 & x \ge 4 \end{cases}$
If the median of $X$ is $3$, then what is the value of $t$? - The elements of the dataset $\{-5,1, a, 5, b\}$ are in ascending order. If both mean and median of the dataset are equal to 3, what is the value of $b$?
- 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 above frequency chart shows the frequency distribution of marks obtained by a set of students in an exam. From the data presented above, which one of the following is CORRECT?
