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Match List-I with List-II

%5Cbegin%7Barray%7D%7B%7Cc%7Cc%7C%7D%20%5Chline%20%5Ctextbf%7BConcepts%7D%20%26%20%5Ctextbf%7BFormula%7D%20%5C%5C%20%5Chline%20%5Ctext%7B(A)%20Weighted%20Mean%7D%20%26%20%5Ctext%7B(I)%20%5C(%5Cfrac%7B%5Csum_%7Bi%3D1%7D%5E%7Bn%7D%20w_i%20x_i%7D%7B%5Csum_%7Bi%3D1%7D%5E%7Bn%7D%20w_i%7D%5C)%20%7D%20%5C%5C%20%5Chline%20%5Ctext%7B(B)%20Grand%20Mean%20of%20Combined%20Data%7D%20%26%20%5Ctext%7B(II)%20%5C(%5Cfrac%7B%5Csum_%7Bi%3D1%7D%5E%7Bn%7D%20x_i%7D%7Bn%7D%5C)%20%7D%20%5C%5C%20%5Chline%20%5Ctext%7B(C)%20Harmonic%20Mean%7D%20%26%20%5Ctext%7B(III)%20%5C(%5Cfrac%7Bn%7D%7B%5Csum_%7Bi%3D1%7D%5E%7Bn%7D%20%5Cfrac%7B1%7D%7Bx_i%7D%7D%5C)%20%7D%20%5C%5C%20%5Chline%20%5Ctext%7B(D)%20Geometric%20Mean%7D%20%26%20%5Ctext%7B(IV)%20%5C(%5Cleft(%20%5Cprod_%7Bi%3D1%7D%5E%7Bn%7D%20x_i%20%5Cright)%5E%7B1%2Fn%7D%5C)%20%7D%20%5C%5C%20%5Chline%20%5Cend%7Barray%7D

Choose the correct answer from the options given below:

Step 1: Understanding the concepts and formulas.
1. **Weighted Mean (A):** The weighted mean is used when each value in a data set has a different level of importance or weight. The formula is: $%5Ctext%7BWeighted%20Mean%7D%20%3D%20%5Cfrac%7B%5Csum_%7Bi%3D1%7D%5E%7Bn%7D%20w_i%20x_i%7D%7B%5Csum_%7Bi%3D1%7D%5E%7Bn%7D%20w_i%7D$ where $w_i$ are the weights, and $x_i$ are the values. This corresponds to **(I)** in List-II.
2. **Grand Mean of Combined Data (B):** The grand mean is the weighted average of the means of several groups. The formula is: $%5Ctext%7BGrand%20Mean%7D%20%3D%20%5Cfrac%7B%5Csum_%7Bi%3D1%7D%5E%7Bn%7D%20x_i%7D%7Bn%7D$ where $x_i$ are the values and $n$ is the total number of observations. This corresponds to **(II)** in List-II.
3. **Harmonic Mean (C):** The harmonic mean is the reciprocal of the arithmetic mean of the reciprocals. The formula is: $%5Ctext%7BHarmonic%20Mean%7D%20%3D%20%5Cfrac%7Bn%7D%7B%5Csum_%7Bi%3D1%7D%5E%7Bn%7D%20%5Cfrac%7B1%7D%7Bx_i%7D%7D$ where $x_i$ are the values and $n$ is the total number of observations. This corresponds to **(III)** in List-II.
4. **Geometric Mean (D):** The geometric mean is the $n$ -th root of the product of $n$ values. The formula is: $%5Ctext%7BGeometric%20Mean%7D%20%3D%20%5Cleft(%20%5Cprod_%7Bi%3D1%7D%5E%7Bn%7D%20x_i%20%5Cright)%5E%7B1%2Fn%7D$ where $x_i$ are the values and $n$ is the total number of observations. This corresponds to **(IV)** in List-II.

Step 2: Matching the concepts with formulas.
- (A) **Weighted Mean** corresponds to formula **(I)**. - (B) **Grand Mean of Combined Data** corresponds to formula **(II)**. - (C) **Harmonic Mean** corresponds to formula **(III)**. - (D) **Geometric Mean** corresponds to formula **(IV)**.

Step 3: Conclusion.
The correct answer is **2. (A) - (I), (B) - (II), (C) - (III), (D) - (IV)**.

High-Yield Trend

Chapter Questions
3 MCQs

Official Solution

Official Solution

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High-Yield Trend

Chapter Questions 3 MCQs

Official Solution

Official Solution

Official Solution

Chapter Questions
3 MCQs