Questions: Question Given the relative frequency table below, which of the following is the corresponding cumulative relative frequency table? Value Relative Frequency 4 0.28 5 0.24 6 0.04 7 0.2 8 0.24

Question
Given the relative frequency table below, which of the following is the corresponding cumulative relative frequency table?
Value Relative Frequency
4 0.28
5 0.24
6 0.04
7 0.2
8 0.24

Transcript text: Question Given the relative frequency table below, which of the following is the corresponding cumulative relative frequency table? \begin{tabular}{|c|c|} \hline Value & \begin{tabular}{c} Relative \\ Frequency \end{tabular} \\ \hline 4 & 0.28 \\ \hline 5 & 0.24 \\ \hline 6 & 0.04 \\ \hline 7 & 0.2 \\ \hline 8 & 0.24 \\ \hline \end{tabular}

Solution

Solution Steps

Step 1: Initialization

The first data value's cumulative relative frequency is the same as its relative frequency. Let's denote the list of data values as \(V = [4, 5, 6, 7, 8]\) and their corresponding relative frequencies as \(RF = [0.28, 0.24, 0.04, 0.2, 0.24]\).

Step 2: Iteration for data value \(V[0] = 4\)

The cumulative relative frequency (CRF) for the first value is directly the relative frequency: \(CRF[0] = RF[0] = 0.28\).

Step 3: Iteration for data value \(V[1] = 5\)

Calculate the cumulative relative frequency for the current data value by adding its relative frequency to the cumulative relative frequency of the previous data value: \(CRF[1] = CRF[0] + RF[1] = 0.28 + 0.24 = 0.52\).

Step 4: Iteration for data value \(V[2] = 6\)

Step 5: Iteration for data value \(V[3] = 7\)

Step 6: Iteration for data value \(V[4] = 8\)

Finalization

The cumulative relative frequency of the last data value equals 1 (or very close to 1, considering rounding errors), validating the correctness of the cumulative relative frequencies calculated.