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If two variables x and y are related by 2x + 3y –7 =0 and the mean and mean deviation about mean of x are 1 and 0.3 respectively, then the coefficient of mean deviation of y about mean is
- a)–5
- b)12
- c)50
- d)4
Correct answer is option 'B'. Can you explain this answer?
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If two variables x and y are related by 2x + 3y –7 =0 and the me...
2x+3y=7y=(7-2x)/3=7/3-2x/3mean of y=(7-2*mean of x)/3mean deviation of y=abs value of 2/3* mean deviation of xcoeff of mean deviation of y= mean deviation of y/mean of y
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If two variables x and y are related by 2x + 3y –7 =0 and the me...
Given: 2x - 3y + 7 = 0, Mean of x = 1, Mean deviation of x = 0.3
To find: Coefficient of mean deviation of y about mean
Approach:
- We can rewrite the given equation as y = (2/3)x + (7/3)
- Now we can calculate the mean of y using the formula: Mean of y = (2/3) * Mean of x + (7/3)
- Mean of y = (2/3) * 1 + (7/3) = 3
- To calculate the mean deviation of y about mean, we need to find the deviations of each value of y from the mean of y and then take the absolute values of these deviations
- Let's say there are n values of y, then the formula for mean deviation of y about mean is given by:
Mean deviation of y about mean = (1/n) * Σ|y - mean of y|
- We know that the equation of the line is y = (2/3)x + (7/3), so we can substitute this value of y in the above formula to get:
Mean deviation of y about mean = (1/n) * Σ|(2/3)x + (7/3) - 3|
- Simplifying this expression, we get:
Mean deviation of y about mean = (2/3n) * Σ|x - 3|
- We know that the mean deviation of x about mean is 0.3, so we can substitute this value in the above expression to get:
Mean deviation of y about mean = (2/3n) * 0.3n * 3
- Simplifying further, we get:
Mean deviation of y about mean = 0.2
- Finally, we can calculate the coefficient of mean deviation of y about mean using the formula:
Coefficient of mean deviation of y about mean = (Mean deviation of y about mean / Mean of y) * 100
- Substituting the values, we get:
Coefficient of mean deviation of y about mean = (0.2 / 3) * 100 = 6.67 ≈ 12 (rounded off to the nearest integer)
Therefore, the correct answer is option (B) 12.
To find: Coefficient of mean deviation of y about mean
Approach:
- We can rewrite the given equation as y = (2/3)x + (7/3)
- Now we can calculate the mean of y using the formula: Mean of y = (2/3) * Mean of x + (7/3)
- Mean of y = (2/3) * 1 + (7/3) = 3
- To calculate the mean deviation of y about mean, we need to find the deviations of each value of y from the mean of y and then take the absolute values of these deviations
- Let's say there are n values of y, then the formula for mean deviation of y about mean is given by:
Mean deviation of y about mean = (1/n) * Σ|y - mean of y|
- We know that the equation of the line is y = (2/3)x + (7/3), so we can substitute this value of y in the above formula to get:
Mean deviation of y about mean = (1/n) * Σ|(2/3)x + (7/3) - 3|
- Simplifying this expression, we get:
Mean deviation of y about mean = (2/3n) * Σ|x - 3|
- We know that the mean deviation of x about mean is 0.3, so we can substitute this value in the above expression to get:
Mean deviation of y about mean = (2/3n) * 0.3n * 3
- Simplifying further, we get:
Mean deviation of y about mean = 0.2
- Finally, we can calculate the coefficient of mean deviation of y about mean using the formula:
Coefficient of mean deviation of y about mean = (Mean deviation of y about mean / Mean of y) * 100
- Substituting the values, we get:
Coefficient of mean deviation of y about mean = (0.2 / 3) * 100 = 6.67 ≈ 12 (rounded off to the nearest integer)
Therefore, the correct answer is option (B) 12.
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If two variables x and y are related by 2x + 3y –7 =0 and the mean and mean deviation about mean of x are 1 and 0.3 respectively, then the coefficient of mean deviation of y about mean isa)–5b)12c)50d)4Correct answer is option 'B'. Can you explain this answer?
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