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Math  /  Data & Statistics

QuestionHeight and weight: A national public health agency study states that the mean height for adult men in the United States is 66.7 inches with a standard deviation of 4.1 inches, and the mean weight is 184.3 pounds with a standard deviation of 38.1 pounds.
Part: 0/30 / 3
Part 1 of 3 (a) Compute the coefficient of variation for height. Round the answer to at least three decimal places.
The coefficient of variation for height is □\square

Studdy Solution

STEP 1

1. The mean height for adult men in the United States is μh=66.7\mu_h = 66.7 inches.
2. The standard deviation of the height is σh=4.1\sigma_h = 4.1 inches.
3. The coefficient of variation (CV) is defined as the ratio of the standard deviation to the mean, often expressed as a percentage.

STEP 2

1. Define the formula for the coefficient of variation.
2. Substitute the given values into the formula.
3. Calculate the coefficient of variation.
4. Round the answer to at least three decimal places.

STEP 3

Define the formula for the coefficient of variation (CV).
CV=(σμ)×100 CV = \left( \frac{\sigma}{\mu} \right) \times 100
Where σ\sigma is the standard deviation and μ\mu is the mean.

STEP 4

Substitute the given values into the formula.
CVh=(4.166.7)×100 CV_h = \left( \frac{4.1}{66.7} \right) \times 100

STEP 5

Calculate the coefficient of variation.
CVh=(4.166.7)×100≈6.146 CV_h = \left( \frac{4.1}{66.7} \right) \times 100 \approx 6.146

STEP 6

Round the answer to at least three decimal places.
CVh≈6.146 CV_h \approx 6.146
The coefficient of variation for height is 6.1466.146.

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