Question

dont drink and drive: a highway safety council reported that there were fatalities among drivers in auto accidents in a particular year frequency distribution of their ages. approximate the mean age. round answer to one decimal place.

age	number of fatalities
21-30	1544
31-40	827
41-50	693
51-60	429
61-70	130

send data to excel

the mean is approximately blank.

Explanation:

Step1: Find midpoints of each age group

For a group \(a - b\), midpoint \(x=\frac{a + b}{2}\).

• 11 - 20: \(x_1=\frac{11 + 20}{2}=15.5\)
• 21 - 30: \(x_2=\frac{21 + 30}{2}=25.5\)
• 31 - 40: \(x_3=\frac{31 + 40}{2}=35.5\)
• 41 - 50: \(x_4=\frac{41 + 50}{2}=45.5\)
• 51 - 60: \(x_5=\frac{51 + 60}{2}=55.5\)
• 61 - 70: \(x_6=\frac{61 + 70}{2}=65.5\)

Step2: Multiply midpoints by frequencies (\(f\))

• \(x_1f_1 = 15.5\times319 = 4944.5\)
• \(x_2f_2 = 25.5\times1544 = 39372\)
• \(x_3f_3 = 35.5\times827 = 29358.5\)
• \(x_4f_4 = 45.5\times693 = 31531.5\)
• \(x_5f_5 = 55.5\times429 = 23809.5\)
• \(x_6f_6 = 65.5\times130 = 8515\)

Step3: Sum the products and total frequency

Sum of products: \(4944.5+39372 + 29358.5+31531.5+23809.5+8515=137531\)
Total frequency: \(319 + 1544+827+693+429+130 = 3942\)

Step4: Calculate the mean (\(\bar{x}=\frac{\sum xf}{\sum f}\))

\(\bar{x}=\frac{137531}{3942}\approx34.9\)

Answer:

34.9