Question

math 175 fall 2025 name: gabriela villar 1 - 29 - 2025
exam i
show all work for partial credit. do not just put down the answer from your calculator!!! you may use excel as a calculator; do not use data analysis package!
the last page is a cheat sheet that might save you some time.
make sure this exam has 4 sheets and 10 questions.

1. (10 pts) (sec 2.1 #8) identify the class width, class midpoints and class boundaries for the frequency distribution. also, identify the number of individuals included in the summary.

Explanation:

Step1: Recall definitions

Class - width is the difference between consecutive lower - class limits. Class mid - points are the average of the lower and upper class limits. Class boundaries are the values that separate classes without gaps. The number of individuals is the sum of the frequencies. Since the frequency distribution is not given here, we assume a general approach. Let's say we have a frequency distribution with lower class limits \(L_1,L_2,\cdots\) and upper class limits \(U_1,U_2,\cdots\) and frequencies \(f_1,f_2,\cdots\).

Step2: Calculate class - width

If the lower class limits are \(L_i\) and \(L_{i + 1}\), the class - width \(w=L_{i+1}-L_i\).

Step3: Calculate class mid - points

The class mid - point \(M_i=\frac{L_i + U_i}{2}\) for each class \(i\).

Step4: Calculate class boundaries

The lower class boundary of a class is the average of the upper limit of the previous class and the lower limit of the current class. The upper class boundary of a class is the average of the upper limit of the current class and the lower limit of the next class. For the first class, the lower class boundary is \(L_1-\frac{1}{2}\) (assuming a non - fractional data set with a gap of 1 between consecutive values in the raw data) and for the last class, the upper class boundary is \(U_n+\frac{1}{2}\).

Step5: Calculate number of individuals

The number of individuals \(N=\sum_{i = 1}^{n}f_i\), where \(n\) is the number of classes.

Answer:

Without the actual frequency distribution data, we cannot provide numerical values for class width, class mid - points, class boundaries and the number of individuals. But the methods to calculate them are as described above.