Question
The marks obtained by a set of students are: 38, 84, 45, 70, 75, 60, 48.
The mean and median marks, respectively, are
The correct answer is
60 and 60
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.
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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?
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