Find the mean of the data summarized in the given frequency distribution.
-The highway speeds of 100 cars are summarized in the frequency distribution below. Find the mean speed. $$\begin{array} { r | r }
\text { Speed (mph) } & \text { Cars } \
\hline 30 - 39 & 3 \
40 - 49 & 17 \
50 - 59 & 51 \
60 - 69 & 16 \
70 - 79 & 13
\end{array}$$
A)59.2 mph
B)54.5 mph
C)62.0 mph
D)56.4 mph

Question

Find the mean of the data summarized in the given frequency distribution.
-The highway speeds of 100 cars are summarized in the frequency distribution below. Find the mean speed. $$\begin{array} { r | r } 
\text { Speed (mph) } & \text { Cars } \
\hline 30 - 39 & 3 \
40 - 49 & 17 \
50 - 59 & 51 \
60 - 69 & 16 \
70 - 79 & 13
\end{array}$$
A)59.2 mph
B)54.5 mph
C)62.0 mph
D)56.4 mph

Quizplus · Accepted Answer

To find the mean speed, we first calculate the midpoint of each speed interval by averaging the upper and lower bounds. Then, we multiply each midpoint by the number of cars in that interval and sum these products. Finally, we divide by the total number of cars.Midpoints: (30+39)/2 = 34.5, (40+49)/2 = 44.5, (50+59)/2 = 54.5, (60+69)/2 = 64.5, (70+79)/2 = 74.5.Multiplying midpoints by the number of cars: 34.5*3 = 103.5, 44.5*17 = 756.5, 54.5*51 = 2779.5, 64.5*16 = 1032, 74.5*13 = 968.5.Sum of products: 103.5 + 756.5 + 2779.5 + 1032 + 968.5 = 5640.Mean speed = Total of products / Total number of cars = 5640 / 100 = 56.4 mph.

Find the Mean of the Data Summarized in the Given