Question

residents in a city are charged for water usage every three months. the water bill is computed from a common fee, along with the amount of water the customers use. the last water bills for 40 neighborhood residents are displayed in the histogram below. which interval shows the greatest change in number of water bills received compared to its previous interval? $150 - $175 $175 - $200 $200 - $225 $225 - $250

Explanation:

Step1: Find the frequency of each interval

Assume the frequencies (from left - right intervals \(100 - 125\), \(125 - 150\), \(150 - 175\), \(175 - 200\), \(200 - 225\), \(225 - 250\)) are \(f_1,f_2,f_3,f_4,f_5,f_6\). Let's estimate the frequencies from the histogram: \(f_1 = 1\), \(f_2=2\), \(f_3 = 5\), \(f_4 = 10\), \(f_5=13\), \(f_6 = 9\).

Step2: Calculate the change between consecutive intervals

• For the interval \(150 - 175\) (previous interval \(125 - 150\)): The change is \(f_3 - f_2=5 - 2 = 3\).
• For the interval \(175 - 200\) (previous interval \(150 - 175\)): The change is \(f_4 - f_3=10 - 5=5\).
• For the interval \(200 - 225\) (previous interval \(175 - 200\)): The change is \(f_5 - f_4=13 - 10 = 3\).
• For the interval \(225 - 250\) (previous interval \(200 - 225\)): The change is \(|f_6 - f_5|=|9 - 13| = 4\).

Answer:

\(\$175 - \$200\)