To calculate the approximate mean age of the fatalities, we will use the midpoints of each age interval and weight them by the number of fatalities in each interval.
First, let's calculate the midpoints for each age group:
- For age group 11-20: Midpoint = \( \frac{11 + 20}{2} = 15.5 \)
- For age group 21-30: Midpoint = \( \frac{21 + 30}{2} = 25.5 \)
- For age group 31-40: Midpoint = \( \frac{31 + 40}{2} = 35.5 \)
- For age group 41-50: Midpoint = \( \frac{41 + 50}{2} = 45.5 \)
- For age group 51-60: Midpoint = \( \frac{51 + 60}{2} = 55.5 \)
- For age group 61-70: Midpoint = \( \frac{61 + 70}{2} = 65.5 \)
Next, we'll multiply each midpoint by the number of fatalities in that age group and sum those products:
\[ \begin{align*} \text{Total} = (15.5 \times 327) + (25.5 \times 1545) + (35.5 \times 860) + \ (45.5 \times 691) + (55.5 \times 423) + (65.5 \times 146) \end{align*} \]
Now, calculate each term:
- \( 15.5 \times 327 = 5078.5 \)
- \( 25.5 \times 1545 = 39397.5 \)
- \( 35.5 \times 860 = 30530 \)
- \( 45.5 \times 691 = 31480.5 \)
- \( 55.5 \times 423 = 23476.5 \)
- \( 65.5 \times 146 = 9583 \)
Now sum the products:
\[ 5078.5 + 39397.5 + 30530 + 31480.5 + 23476.5 + 9583 = 127,145 \]
Next, sum the total number of fatalities, which is given as 3992.
Finally, to find the mean age, we divide the total from our previous calculations by the total number of fatalities:
\[ \text{Mean Age} = \frac{127145}{3992} \approx 31.9 \]
Thus, the approximate mean age of the drivers in the reported fatalities is 31.9 years (rounded to one decimal place).
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