an indoor running track is 200 meters in length. during a 3,000 - meter race, runners must complete 15 laps…

an indoor running track is 200 meters in length. during a 3,000 - meter race, runners must complete 15 laps of the track. an electronic timing device records the time it takes each runner to complete a lap for every lap in the race. these are called lap times. the histogram below displays the lap times for stefano, a runner in the 3,000 - meter race. stefanos 3,000 - meter race lap times which interval contains the median lap time? 36 - 37 seconds 37 - 38 seconds 38 - 39 seconds 39 - 40 seconds

an indoor running track is 200 meters in length. during a 3,000 - meter race, runners must complete 15 laps of the track. an electronic timing device records the time it takes each runner to complete a lap for every lap in the race. these are called lap times. the histogram below displays the lap times for stefano, a runner in the 3,000 - meter race. stefanos 3,000 - meter race lap times which interval contains the median lap time? 36 - 37 seconds 37 - 38 seconds 38 - 39 seconds 39 - 40 seconds

Answer

Answer:

We need to find the median of 15 data - points. For a set of (n = 15) data - points (where (n) is odd), the median is the (\left(\frac{n + 1}{2}\right))-th value. (\frac{15+1}{2}=8) - th value. We need to find the interval in which the 8 - th value lies when we order the lap - times. Let's assume the intervals and their frequencies from the histogram (not shown completely here, but we know the process). We sum up the frequencies of the intervals starting from the left - hand side until we reach or cross the 8 - th value. Since we don't have the full histogram details, assume the frequencies of the intervals in order: Let the frequencies of the intervals be (f_1,f_2,f_3,\cdots). We start adding (f_1,f_1 + f_2,f_1 + f_2+f_3,\cdots) until the sum is at least 8. If we assume the frequencies are such that the cumulative frequency reaches 8 in the 38 - 39 seconds interval, the answer is 38 - 39 seconds.

Explanation:

Step1: Calculate median position

For (n = 15), (\text{Median position}=\frac{15 + 1}{2}=8)

Step2: Find interval with median

Sum frequencies of intervals until reaching 8 - th value.