Math Problem Statement

Times Spent in Rush-Hour Traffic: A sample of 13 drivers shows the time that they spent (in minutes) stopped in rush-hour traffic on a specific snowy day last winter. The problem asks to find the range, variance, and standard deviation of the given data.

Solution

The image shows a set of traffic data for 13 drivers and their time spent in rush-hour traffic, with the following questions:

  1. Find the range (which is correctly provided as 27).
  2. Find the variance, which is calculated as 87.24359.
  3. Find the standard deviation, which is not yet filled in.

To calculate the standard deviation:

The standard deviation (σ) is the square root of the variance (σ²).

σ=Variance=87.24359\sigma = \sqrt{\text{Variance}} = \sqrt{87.24359}

Let me calculate that for you.The standard deviation is approximately 9.3 (rounded to one decimal place).

Would you like further clarification or details on any of the steps?

Here are 5 related questions to consider:

  1. What is the interpretation of the range in this context?
  2. How does variance differ from standard deviation in terms of meaning?
  3. What effect does having an outlier in the data set have on the variance and standard deviation?
  4. Can you explain how to calculate the mean of this data set?
  5. Why is it important to round answers in statistical analysis?

Tip: The standard deviation gives you a sense of how spread out the values in a data set are, with a larger standard deviation indicating more variability.

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Math Problem Analysis

Mathematical Concepts

Statistics
Variance
Standard Deviation
Range

Formulas

Range = Max - Min
Variance (σ²) = Σ (x - μ)² / N
Standard Deviation (σ) = √Variance

Theorems

Range measures the spread of data.
Variance calculates the average of the squared differences from the mean.
Standard deviation is the square root of variance and shows how much the data deviates from the mean.

Suitable Grade Level

High School Statistics