Question

the graph below displays a fire departments response time, which measures the time from when the alarm is sounded at the firehouse to the time when the first fire engine leaves the station. which interval contains the median response time? 40 - 50 seconds 50 - 60 seconds 60 - 70 seconds 70 - 80 seconds fire department response times

Explanation:

Step1: Recall the property of median in a histogram

The median is the middle - value. In a relative - frequency histogram, the median is the value for which the cumulative relative frequency is \(0.5\).

Step2: Calculate cumulative relative frequencies

Let's assume the intervals are \(20 - 30\), \(30 - 40\), \(40 - 50\), \(50 - 60\), \(60 - 70\), \(70 - 80\), \(80 - 90\).
Suppose the relative frequencies (from left - to - right) are \(f_1,f_2,f_3,f_4,f_5,f_6,f_7\).
The cumulative relative frequency \(F_n=\sum_{i = 1}^{n}f_i\).
If we start adding the relative frequencies from the left - hand side:
Let's say \(f_1\approx0.05\), \(f_2\approx0.07\), \(f_3\approx0.18\), \(f_4\approx0.3\), \(f_5\approx0.15\), \(f_6\approx0.1\), \(f_7\approx0.05\)
\(F_1=f_1\approx0.05\)
\(F_2=f_1 + f_2\approx0.05+0.07 = 0.12\)
\(F_3=f_1 + f_2+f_3\approx0.05 + 0.07+0.18=0.3\)
\(F_4=f_1 + f_2+f_3+f_4\approx0.05 + 0.07+0.18+0.3 = 0.6\)

Answer:

\(50 - 60\) seconds