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Statement-1 : The mean deviation of the ...

Statement-1 : The mean deviation of the numbers `3,4,5,6,7` is `1.2`
Statement-2 : Mean deviation =`(Sigma_(i=1)^(n) |x_i-barx|)/n`.

A

a) Both statement I and statement II are correct. Statement II is the correct explanation of statement I.

B

b) Both statement I and statement II are correct. Statement II is not the correct explanation of statement I.

C

c) Statement I is correct and statement II is incorrect.

D

d) Statement I is incorrect and statement II is correct.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to verify the two statements regarding the mean deviation of the numbers 3, 4, 5, 6, and 7. ### Step-by-Step Solution: 1. **Calculate the Mean (x̄)**: - The mean is calculated using the formula: \[ \bar{x} = \frac{\sum_{i=1}^{n} x_i}{n} \] - Here, the numbers are 3, 4, 5, 6, and 7. The total number of items (n) is 5. - Calculate the sum: \[ 3 + 4 + 5 + 6 + 7 = 25 \] - Now, calculate the mean: \[ \bar{x} = \frac{25}{5} = 5 \] 2. **Calculate the Mean Deviation**: - The formula for mean deviation is: \[ \text{Mean Deviation} = \frac{\sum_{i=1}^{n} |x_i - \bar{x}|}{n} \] - Substitute the values: \[ \text{Mean Deviation} = \frac{|3 - 5| + |4 - 5| + |5 - 5| + |6 - 5| + |7 - 5|}{5} \] - Calculate each absolute difference: - \(|3 - 5| = 2\) - \(|4 - 5| = 1\) - \(|5 - 5| = 0\) - \(|6 - 5| = 1\) - \(|7 - 5| = 2\) - Now sum these values: \[ 2 + 1 + 0 + 1 + 2 = 6 \] - Finally, calculate the mean deviation: \[ \text{Mean Deviation} = \frac{6}{5} = 1.2 \] 3. **Verify the Statements**: - **Statement 1**: The mean deviation of the numbers 3, 4, 5, 6, 7 is 1.2. (True) - **Statement 2**: Mean deviation = \(\frac{\sum_{i=1}^{n} |x_i - \bar{x}|}{n}\). (True) Since both statements are true, and Statement 2 correctly explains how to compute the mean deviation, we conclude that: ### Final Answer: Both Statement 1 and Statement 2 are correct, and Statement 2 is the correct explanation of Statement 1. ### Correct Option: Option A: Both statement 1 and statement 2 are correct. Statement 2 is the correct explanation of statement 1. ---
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