Question

Match the following statistical terms with the suitable explanation

List-I (Statistical term)	List-II (Explanation)
(A) Mode	(I) just the $50^{\text{th}}$ percentile value below which 50% of the values in the sample fall
(B) Median	(II) value of a variable is compared with a constant quantity of another variable
(C) Geometric mean	(III) value around which the items tend to be most heavily concentrated
(D) Harmonic mean	(IV) averaging ratio & percentages and computing average rates of increase or decrease

Choose the correct answer from the options given below

• (A) - (III), (B) - (I), (C) - (IV), (D) - (II)
• (A) - (II), (B) - (IV), (C) - (I), (D) - (III)
• (A) - (IV), (B) - (I), (C) - (II), (D) - (III)
• (A) - (I), (B) - (II), (C) - (IV), (D) - (III)

Hint:

To remember the applications of different means:
Geometric Mean = Ratios, percentages, growth rates (IV).
Harmonic Mean = Rates, speed, unit comparisons (II).
Median = 50th percentile (I).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
In statistics, measures of central tendency provide a single value that represents the center or typical value of a data set.
Each measure—such as the mean, median, mode, geometric mean, and harmonic mean—has unique mathematical properties and applications.

Step 2: Detailed Explanation:
Let us analyze and match each statistical term:
1.Mode (A): The mode is the value that occurs most frequently in a data set.
It represents the value around which observations tend to be most heavily concentrated.
Thus, (A) matches with (III).
2.Median (B): The median is the middle value when the data set is arranged in ascending order.
It represents the 50th percentile, meaning exactly 50% of the values fall below it.
Thus, (B) matches with (I).
3.Geometric mean (C): The geometric mean is calculated as the \( n \)-th root of the product of \( n \) numbers.
It is the standard measure used for averaging ratios, percentages, and growth rates over time.
Thus, (C) matches with (IV).
4.Harmonic mean (D): The harmonic mean is the reciprocal of the arithmetic mean of the reciprocals of the data points.
It is used when a variable is compared with a constant quantity of another variable, such as calculating average speeds (distance/time) or rates of work.
Thus, (D) matches with (II).
Combining these matches:
\[ \text{(A)-(III), (B)-(I), (C)-(IV), (D)-(II)} \]

Step 3: Final Answer:
The correct matching sequence is (A) - (III), (B) - (I), (C) - (IV), (D) - (II).