Horatio Oscar Vineeth Lane (HOV Lane for short) records his commute times for a period of one month and assigned them to five different categories as shown in the table.
$$\begin{array} { | c | c | }
\hline \text { Commute Length } & \text { Number af Observations } \
\hline \text { commute time }

Question

Horatio Oscar Vineeth Lane (HOV Lane for short) records his commute times for a period of one month and assigned them to five different categories as shown in the table.
 $$\begin{array} { | c | c | } 
\hline \text { Commute Length } & \text { Number af Observations } \
\hline \text { commute time } < 10 \text { minutes } & 1 \
\hline 10 \leq \text { commute time } < 20 \text { minutes } & 2 \
\hline 20 \leq \text { commute time } < 30 \text { minutes } & 4 \
\hline 30 \leq \text { commute time } < 40 \text { minutes } & 9 \
\hline 40 \leq \text { commute time } < 50 \text { minutes } & 4 \
\hline
\end{array}$$
-What is the duration of Mr. Lane's expected commute?

Quizplus · Accepted Answer

The expected commute time is the mean of the commute times. The mean is calculated by multiplying the midpoint of each interval by the number of observations in that interval, and then dividing the sum of these products by the total number of observations.For the first interval, the midpoint is 5 minutes and the number of observations is 1, so the product is 5. For the second interval, the midpoint is 15 minutes and the number of observations is 2, so the product is 30. For the third interval, the midpoint is 25 minutes and the number of observations is 4, so the product is 100. For the fourth interval, the midpoint is 35 minutes and the number of observations is 9, so the product is 315. For the fifth interval, the midpoint is 45 minutes and the number of observations is 4, so the product is 180.The total number of observations is 1 + 2 + 4 + 9 + 4 = 20. So the mean is (5 + 30 + 100 + 315 + 180) / 20 = 630 / 20 = 31.5 minutes.

Horatio Oscar Vineeth Lane (HOV Lane for Short) Records His