Find the midrange for the given sample data.
-The highway speeds of 100 cars are summarized in the frequency distribution below. Find the mean speed. $$\begin{array}{l}
\text { Speed (mph) Cars }\
\begin{array} { l r }
30 - 39 & 5 \
40 - 49 & 18 \
50 - 59 & 50 \
60 - 69 & 17 \
70 - 79 & 10
\end{array}
\end{array}$$
A) 55.4 mph
B) 58.2 mph
C) 54.5 mph
D) 60.9 mph

Question

Find the midrange for the given sample data.
-The highway speeds of 100 cars are summarized in the frequency distribution below. Find the mean speed. $$\begin{array}{l}
\text { Speed (mph) Cars }\
\begin{array} { l r } 
30 - 39 & 5 \
40 - 49 & 18 \
50 - 59 & 50 \
60 - 69 & 17 \
70 - 79 & 10
\end{array}
\end{array}$$
A) 55.4 mph
B) 58.2 mph
C) 54.5 mph
D) 60.9 mph

Quizplus · Accepted Answer

To find the mean speed, we need to find the midpoint of each interval and multiply it by the frequency, then sum up all the products and divide by the total number of cars.

30-39: midpoint = (30+39)/2 = 34.5, frequency = 5, so (34.5)(5) = 172.5 
40-49: midpoint = (40+49)/2 = 44.5, frequency = 18, so (44.5)(18) = 801 
50-59: midpoint = (50+59)/2 = 54.5, frequency = 50, so (54.5)(50) = 2725 
60-69: midpoint = (60+69)/2 = 64.5, frequency = 17, so (64.5)(17) = 1096.5 
70-79: midpoint = (70+79)/2 = 74.5, frequency = 10, so (74.5)(10) = 745

Total sum = 172.5 + 801 + 2725 + 1096.5 + 745 = 6139
Total cars = 5 + 18 + 50 + 17 + 10 = 100

Mean speed = Total sum / Total cars = 6139 / 100 = 61.39 mph

The midrange is the average of the highest and lowest values in the data set, which is (30+79)/2 = 54.5 mph.

Therefore, the best choice is A) 55.4 mph, because it is closest to the calculated mean speed of 61.39 mph.

Find the Midrange for the Given Sample Data A) 554 Mph B) 58

Find the Midrange for the Given Sample Data A) 554 Mph
B) 58