The highway speeds of 100 cars are summarized in the frequency distribution below. Find the grouped mean rounded to the nearest tenth of a mile per hour. $$\begin{array} { r | r }
\text { Speed (mph) } & \text { Cars } \
\hline 30 - 39 & 3 \
40 - 49 & 19 \
50 - 59 & 51 \
60 - 69 & 17 \
70 - 79 & 10
\end{array}$$
A) 58.5 mph
B) 54.5 mph
C) 55.7 mph
D) 61.3 mph

Question

The highway speeds of 100 cars are summarized in the frequency distribution below. Find the grouped mean rounded to the nearest tenth of a mile per hour. $$\begin{array} { r | r } 
\text { Speed (mph) } & \text { Cars } \
\hline 30 - 39 & 3 \
40 - 49 & 19 \
50 - 59 & 51 \
60 - 69 & 17 \
70 - 79 & 10
\end{array}$$
A) 58.5 mph
B) 54.5 mph
C) 55.7 mph
D) 61.3 mph

Quizplus · Accepted Answer

To find the grouped mean, we first calculate the midpoint of each speed range by averaging the lower and upper bounds. Then, we multiply each midpoint by the number of cars in that speed range, sum these products, and divide by the total number of cars. The calculations are as follows:- For 30-39 mph: Midpoint = (30+39)/2 = 34.5; Product = 34.5 * 3 = 103.5- For 40-49 mph: Midpoint = (40+49)/2 = 44.5; Product = 44.5 * 19 = 845.5- For 50-59 mph: Midpoint = (50+59)/2 = 54.5; Product = 54.5 * 51 = 2780- For 60-69 mph: Midpoint = (60+69)/2 = 64.5; Product = 64.5 * 17 = 1096.5- For 70-79 mph: Midpoint = (70+79)/2 = 74.5; Product = 74.5 * 10 = 745Total Product = 103.5 + 845.5 + 2780 + 1096.5 + 745 = 5571Total Cars = 3 + 19 + 51 + 17 + 10 = 100Grouped Mean = Total Product / Total Cars = 5571 / 100 = 55.71 mphRounded to the nearest tenth, the grouped mean speed is 55.7 mph.

The Highway Speeds of 100 Cars Are Summarized in the Frequency