alex records the running time—the number of minutes a movie lasts from start to finish—of 50 popular movies…

alex records the running time—the number of minutes a movie lasts from start to finish—of 50 popular movies. the distribution of times, in minutes, is shown in the histogram below. which interval contains the median movie run time? 90 - 100 minutes 100 - 110 minutes 110 - 120 minutes 120 - 130 minutes movie running times frequency 16 14 12 10 8 6 4 2 0 70 80 90 100 110 120 130 140 150 160 time (minutes)

alex records the running time—the number of minutes a movie lasts from start to finish—of 50 popular movies. the distribution of times, in minutes, is shown in the histogram below. which interval contains the median movie run time? 90 - 100 minutes 100 - 110 minutes 110 - 120 minutes 120 - 130 minutes movie running times frequency 16 14 12 10 8 6 4 2 0 70 80 90 100 110 120 130 140 150 160 time (minutes)

Answer

Answer:

C. 110 - 120 minutes

Explanation:

Step1: Find the position of the median

There are (n = 50) data - points. For a set of (n) data - points, the median position is (\frac{n + 1}{2}=\frac{50+1}{2}=25.5) (for an even number of data - points, we take the average of the values at positions (\frac{n}{2}) and (\frac{n}{2}+1)). In terms of cumulative frequency, we want to find the interval where the cumulative frequency crosses the 25th and 26th ordered data - points.

Step2: Calculate cumulative frequencies

From the histogram:

  • For the 70 - 80 minutes interval, frequency (f_1=8), cumulative frequency (CF_1 = 8).
  • For the 80 - 90 minutes interval, frequency (f_2 = 16), cumulative frequency (CF_2=8 + 16=24).
  • For the 90 - 100 minutes interval, frequency (f_3 = 14), cumulative frequency (CF_3=24 + 14 = 38).
  • For the 100 - 110 minutes interval, frequency (f_4=12), cumulative frequency (CF_4=38 + 12 = 50). The cumulative frequency crosses the 25th and 26th data - points in the 110 - 120 minutes interval.