Question
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?
The correct answer is
mode > median > mean
To determine the correct relationship between mean, median, and mode from the given frequency distribution, let's analyze the data presented in the frequency chart.
The chart shows the marks (3 to 9) with their corresponding frequencies. Let's calculate the mean, median, and mode.
- Mode: The mode is the value that appears most frequently in a data set. From the chart, mark '7' appears the most with a frequency of 14. Therefore, the mode is 7.
- Median: To find the median, we need to arrange the data in ascending order and find the middle value. Let's calculate the cumulative frequency:
- 3: Frequency = 3
- 4: Frequency = 9, Cumulative Frequency = 12
- 5: Frequency = 11, Cumulative Frequency = 23
- 6: Frequency = 7, Cumulative Frequency = 30
- 7: Frequency = 14, Cumulative Frequency = 44
- 8: Frequency = 2, Cumulative Frequency = 46
- 9: Frequency = 4, Cumulative Frequency = 50
- Both the 25th and 26th observations fall under mark '6' (in the cumulative frequency of 30).
- Mean: The mean is calculated using the formula:
- where \( f \) is the frequency and \( x \) is the mark.
- \( \sum (f \times x) = 3 \times 3 + 9 \times 4 + 11 \times 5 + 7 \times 6 + 14 \times 7 + 2 \times 8 + 4 \times 9 = 316 \)
- \( \sum f = 50 \)
Hence, we have Mode = 7, Median = 6, Mean = 6.32.
The relationship between them is: Mode > Median > Mean.
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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 frequency distribution of beak sizes of a bird species is symmetric but not normally distributed. If the mean value of beak size is 6 mm, standard deviation is 25 mm and kurtosis is 10, then the median is ______ mm.
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