Question

scott is the manager for the touring rock band hi phone. for the bands recently ended summer tour, scott kept track of the attendance of each of the bands concerts. the histogram below summarizes the data. use the histogram to answer each of the questions.
frequency
(number of concerts)
(a) what is the class width?
(b) one class is the least frequent. how many concerts are in this class?
(c) according to the histogram, what is the total number of concerts?

Explanation:

Part (a)

Step1: Identify class intervals

The class intervals are \(50 - 174\), \(175 - 299\), \(300 - 424\), \(425 - 549\).

Step2: Calculate class width

For a class interval \(a - b\), class width is \(b - a+ 1\)? No, for continuous data (like attendance, we can consider it as continuous here), class width is \(b - a\). Take the first interval: \(174 - 50=124\)? Wait, no, \(175 - 50 = 125\)? Wait, let's check the difference between the lower bounds. The lower bounds are 50, 175, 300, 425. The difference between 175 and 50 is \(175 - 50=125\), between 300 and 175 is \(300 - 175 = 125\), between 425 and 300 is \(425 - 300=125\). So class width is \(125\).

Step1: Identify frequencies

From the histogram, the frequencies (number of concerts) for each class: \(50 - 174\): 4, \(175 - 299\): 9, \(300 - 424\): 4, \(425 - 549\): 1.

Step2: Find the least frequent

The least frequency is 1, so the number of concerts in the least frequent class is 1.

Step1: Sum the frequencies

Frequencies are 4 (for \(50 - 174\)), 9 (for \(175 - 299\)), 4 (for \(300 - 424\)), 1 (for \(425 - 549\)).

Step2: Calculate total

Total number of concerts \(=4 + 9+4 + 1=18\).

Answer:

\(125\)

Part (b)