Comparing Variation in Different Data Sets In Exercises 45–50, find the coefficient of variation for each of the two data sets. Then compare the results.
Heights and Weights The heights (in inches) and weights (in pounds) of every France national soccer team player that started the 2018 FIFA Men’s World Cup final are listed. (Source: ESPN)

Verified step by step guidance

1. Step 1: Understand the coefficient of variation (CV). The CV is a measure of relative variability and is calculated as the ratio of the standard deviation (SD) to the mean (μ), expressed as a percentage: CV = (SD / μ) × 100.
2. Step 2: Calculate the mean (μ) for each data set. For the heights, sum all the values and divide by the number of players. Repeat the same process for the weights.
3. Step 3: Calculate the standard deviation (SD) for each data set. Use the formula: SD = sqrt(Σ(xi - μ)^2 / n), where xi represents each individual value, μ is the mean, and n is the number of values in the data set.
4. Step 4: Compute the coefficient of variation (CV) for each data set using the formula CV = (SD / μ) × 100. Perform this calculation separately for the heights and weights.
5. Step 5: Compare the CVs of the two data sets. A higher CV indicates greater relative variability in the data set. Discuss the implications of the comparison in terms of the variability of heights versus weights.

Key Concepts

Coefficient of Variation

The coefficient of variation (CV) is a statistical measure of the relative variability of a data set. It is calculated as the ratio of the standard deviation to the mean, expressed as a percentage. This metric allows for the comparison of the degree of variation between different data sets, regardless of their units or scales, making it particularly useful in fields like finance and quality control.

Standard Deviation

Standard deviation is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range. It is a crucial component in calculating the coefficient of variation, as it quantifies the extent of variability in the data.

Mean

The mean, or average, is a measure of central tendency that is calculated by summing all the values in a data set and dividing by the number of values. It provides a single value that represents the center of the data distribution. In the context of the coefficient of variation, the mean serves as the baseline against which the standard deviation is compared, allowing for a relative assessment of variability.