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Statement-1 : If the mode of the data is...

Statement-1 : If the mode of the data is 18 and the mean is 24, then median is 22
Statement-2 : Mode =3 median -2 mean A.Statement -1 is true , statement -2 is true B.Statement -1 is true but statement -2 is false. C.Statement -1 is false but statement -2 is true. D.none of these

A

Statement -1 is true , statement -2 is true

B

Statement -1 is true but statement -2 is false.

C

Statement -1 is false but statement -2 is true.

D

none of these

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze both statements and verify their validity step by step. ### Step 1: Analyze Statement 1 **Statement 1**: If the mode of the data is 18 and the mean is 24, then the median is 22. We are given: - Mode (Mo) = 18 - Mean (M) = 24 We know the relationship between mode, median, and mean can be expressed as: \[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \] Let’s denote the median as \( \text{Median} = x \). Substituting the known values into the equation: \[ 18 = 3x - 2(24) \] \[ 18 = 3x - 48 \] \[ 3x = 18 + 48 \] \[ 3x = 66 \] \[ x = \frac{66}{3} \] \[ x = 22 \] Thus, the median is indeed 22. Therefore, **Statement 1 is true**. ### Step 2: Analyze Statement 2 **Statement 2**: Mode = 3 × Median - 2 × Mean. We already derived this relationship in the previous step. We can confirm that: \[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \] is a valid statistical formula. Since we have already calculated that: - Mode = 18 - Median = 22 - Mean = 24 Substituting these values into the equation: \[ 18 = 3(22) - 2(24) \] \[ 18 = 66 - 48 \] \[ 18 = 18 \] This confirms that **Statement 2 is also true**. ### Conclusion Both statements are true. Thus, the correct answer is: **A. Statement -1 is true, statement -2 is true.** ---
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