The mean and median marks, respectively, are
Calculating Mean and Median Marks
The problem requires finding the mean and median for the given set of student marks: 38, 84, 45, 70, 75, 60, 48.
Calculating the Mean Marks
The mean (average) is calculated by summing all the marks and dividing by the total number of students.
- Given marks: 38, 84, 45, 70, 75, 60, 48
- Number of students ($n$): 7
- Sum of marks = $38 + 84 + 45 + 70 + 75 + 60 + 48 = 420$
- Mean = $\frac{\text{Sum of marks}}{n}$ = $\frac{420}{7}$ = 60
The mean mark is 60.
Calculating the Median Marks
The median is the middle value in a dataset that is ordered from least to greatest.
- Arrange the marks in ascending order: 38, 45, 48, 60, 70, 75, 84
- Since there are 7 students (an odd number), the median is the middle value.
- The middle position is calculated as $\frac{n+1}{2}$ = $\frac{7+1}{2}$ = $\frac{8}{2}$ = 4th position.
- The mark in the 4th position is 60.
The median mark is 60.
Conclusion
The mean and median marks are 60 and 60, respectively.
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 ________________.
