Question

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

Explanation:

Step1: Find the position of the median

For \(n = 50\) data points, the median is the \(\frac{n + 1}{2}=\frac{50+1}{2}=25.5^{th}\) value. So we need to find the interval where the cumulative frequency first exceeds \(25.5\).

Step2: Calculate cumulative frequencies

• For the \(80 - 90\) interval: frequency \(f_1=8\), cumulative frequency \(CF_1 = 8\)
• For the \(90 - 100\) interval: frequency \(f_2 = 15\), cumulative frequency \(CF_2=8 + 15=23\)
• For the \(100 - 110\) interval: frequency \(f_3=13\), cumulative frequency \(CF_3=23+13 = 36\)

Since \(23<25.5<36\)

Answer:

100 - 110 minutes