Variance of Roller Coaster Speeds The standard deviation of the sample values in Exercise 1 is 43.1 km/h. What is the variance (including units)?

Verified step by step guidance

1. Understand the relationship between standard deviation and variance: Variance is the square of the standard deviation. Mathematically, this is expressed as \( \text{Variance} = (\text{Standard Deviation})^2 \).
2. Identify the given value: The standard deviation is provided as 43.1 km/h.
3. Square the standard deviation to calculate the variance: Use the formula \( \text{Variance} = (43.1)^2 \).
4. Include the correct units: Since the standard deviation is in km/h, the variance will be in \( (\text{km/h})^2 \), or square kilometers per hour squared.
5. Write the final expression for the variance: \( \text{Variance} = 43.1^2 \ \text{km}^2/\text{h}^2 \).

Key Concepts

Standard Deviation

Standard deviation is a measure of the amount of variation or dispersion in a set of values. It indicates how much individual data points deviate from the mean of the dataset. A low standard deviation means 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.

Variance

Variance is the square of the standard deviation and quantifies the degree of spread in a dataset. It is calculated by averaging the squared differences between each data point and the mean. Variance provides insight into the variability of the data, with larger values indicating greater dispersion.

Units of Measurement

Units of measurement are essential for interpreting statistical results accurately. In the context of variance, the units are the square of the original units of the data. For example, if the speeds are measured in kilometers per hour (km/h), the variance will be expressed in square kilometers per hour (km²/h²), which reflects the squared nature of the calculation.