Don't drink and drive: A highway safety council reported that there were 3959 fatalities among drivers in auto accidents in a particular year. Following is a frequency distribution of their ages. Approximate the mean age. Round your answer to one decimal place.
Age | Number of Fatalities
------- | --------
11-20 | 328
21-30 | 1528
31-40 | 861
41-50 | 682
51-60 | 413
61-70 | 147
The mean is approximately what?
Answer (2)
Calculate the midpoint of each age interval.
Multiply each midpoint by the number of fatalities in that interval and sum the products: 15.5 × 328 + 25.5 × 1528 + 35.5 × 861 + 45.5 × 682 + 55.5 × 413 + 65.5 × 147 = 138194.5 .
Divide the sum by the total number of fatalities: 3959 138194.5 ≈ 34.906 .
Round to one decimal place: 34.9 .
Explanation
Understanding the Problem We are given a frequency distribution of the ages of drivers who died in auto accidents and asked to approximate the mean age. To do this, we'll find the midpoint of each age interval, multiply it by the number of fatalities in that interval, sum these products, and then divide by the total number of fatalities.
Calculating Midpoints First, we calculate the midpoint of each age interval:
11-20: 2 11 + 20 = 15.5
21-30: 2 21 + 30 = 25.5
31-40: 2 31 + 40 = 35.5
41-50: 2 41 + 50 = 45.5
51-60: 2 51 + 60 = 55.5
61-70: 2 61 + 70 = 65.5
Calculating Sum of Products Next, we multiply the midpoint of each interval by the number of fatalities in that interval and sum the results: ( 15.5 × 328 ) + ( 25.5 × 1528 ) + ( 35.5 × 861 ) + ( 45.5 × 682 ) + ( 55.5 × 413 ) + ( 65.5 × 147 ) = 5084 + 38964 + 30565.5 + 31031 + 22911.5 + 9638.5 = 138194.5
Calculating the Mean Now, we divide the sum of the products by the total number of fatalities (3959) to find the approximate mean age: 3959 138194.5 ≈ 34.90641576155595
Rounding the Result Finally, we round the result to one decimal place: 34.9
Final Answer The approximate mean age of the drivers who died in auto accidents is 34.9 years.
Examples
Understanding the average age of drivers involved in accidents can help highway safety councils target specific age groups with tailored safety campaigns. For instance, if the mean age is higher than expected, campaigns might focus on older drivers and age-related driving challenges. Conversely, a lower mean age might indicate a need for campaigns targeting younger, less experienced drivers. This data-driven approach allows for more effective allocation of resources and development of impactful safety initiatives.
To find the mean age of drivers involved in fatal accidents, we calculated the midpoints of age intervals, multiplied them by the number of fatalities, summed those products, and divided by the total number of fatalities. This resulted in a mean age of approximately 34.9 years. Rounding the result to one decimal place gives us a clear understanding of the average age of these drivers.
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