Consider the following frequency distribution of an ecological variable: Such a distribution with two peaks is called a bi-modal distribution. Here, the peak with the higher frequency is called the major mode and the one with the lower frequency is called the minor mode. A student has marked four points on the x-axis, i.e., P, Q, R and S. Match the points with the most appropriate statistic: Mean, Median, Major mode, and Minor mode
To solve the given problem, let's understand the concepts involved in a bimodal distribution:
- Mode: In a bimodal distribution, there are two peaks. The peak with the higher frequency is the major mode, and the peak with the lower frequency is the minor mode.
- Mean: The average of the dataset. It lies towards the side of the longer tail in a skewed distribution.
- Median: The middle value when data points are arranged in ascending order. It's less affected by extremes and usually lies between the mean and mode in asymmetrical distributions.
Now, we can analyze the points marked P, Q, R, and S on the x-axis:
- Point P is at the first peak of the distribution, where the frequency is lower. Hence, it represents the Minor Mode.
- Point R is around the center of the data distribution, indicating the balance point. Thus, it represents the Mean.
- Point S is at the highest peak, representing the point with the highest frequency. Therefore, it is the Major Mode.
Based on this analysis, we can match the points as follows: P-Minor mode, R-Mean, S-Major mode.
The correct option is: P-Minor mode, R-Mean, S-Major mode.
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?
