High School

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Make a frequency table showing class limits, class boundaries, midpoints, frequencies, relative frequencies, and cumulative frequencies. (Round your relative frequencies to two decimal places). Start with the lowest class limit of 26.

[tex]
\[
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline
\multicolumn{2}{|c|}{Class Limits} & \multicolumn{2}{c|}{Class Boundaries} & Midpoints & Frequency & Relative Frequency & Cumulative Frequency \\
\hline
Lower & Upper & Lower & Upper & & & & \\
\hline
26 & 36.2 & 25.9 & 36.2 & 31.1 & 4 & 0.05 & 4 \\
\hline
36.3 & 46.4 & 36.2 & 46.4 & 41.1 & 21 & 0.26 & 25 \\
\hline
46.5 & 56.6 & 46.4 & 56.6 & 51.1 & 45 & 0.57 & 70 \\
\hline
56.7 & 66.8 & 56.6 & 66.8 & 61.1 & 7 & 0.09 & 77 \\
\hline
66.9 & 77 & 66.8 & 77.0 & 71.95 & 3 & 0.03 & 80 \\
\hline
\end{tabular}
\]
[/tex]

Note: Ensure the relative frequencies add up to 1.00 for consistency. Adjust values as necessary based on the total sample size.

Answer :

Let's create a frequency table with the provided data. The table will include class limits, class boundaries, midpoints, frequencies, relative frequencies, and cumulative frequencies. Here's how we can build this table step-by-step:

### Step 1: Class Limits
These are given directly:
- Class 1: 26 to 36.2
- Class 2: 36.3 to 46.4
- Class 3: 46.5 to 56.6
- Class 4: 56.7 to 66.8
- Class 5: 66.9 to 77

### Step 2: Class Boundaries
To find the class boundaries, subtract 0.05 from the lower limit and add 0.05 to the upper limit of each class:
- Class 1: 25.95 to 36.25
- Class 2: 36.25 to 46.45
- Class 3: 46.45 to 56.65
- Class 4: 56.65 to 66.85
- Class 5: 66.85 to 77.05

### Step 3: Midpoints
The midpoint can be calculated by averaging the lower and upper class limits:
- Class 1: (26 + 36.2) / 2 = 31.1
- Class 2: (36.3 + 46.4) / 2 = 41.35
- Class 3: (46.5 + 56.6) / 2 = 51.55
- Class 4: (56.7 + 66.8) / 2 = 61.75
- Class 5: (66.9 + 77) / 2 = 71.95

### Step 4: Frequencies
Frequencies are provided:
- Class 1: 4
- Class 2: 21
- Class 3: 45
- Class 4: 7
- Class 5: 3

### Step 5: Relative Frequencies
The relative frequency is found by dividing the frequency of each class by the total number of frequencies:
Total frequency = 4 + 21 + 45 + 7 + 3 = 80

- Class 1: 4 / 80 = 0.05
- Class 2: 21 / 80 ≈ 0.26
- Class 3: 45 / 80 = 0.56
- Class 4: 7 / 80 ≈ 0.09
- Class 5: 3 / 80 ≈ 0.04

### Step 6: Cumulative Frequencies
This is the running total of frequencies:
- Class 1: 4
- Class 2: 4 + 21 = 25
- Class 3: 25 + 45 = 70
- Class 4: 70 + 7 = 77
- Class 5: 77 + 3 = 80

### Final Frequency Table
```
| Class Limits | Class Boundaries | Midpoints | Frequency | Relative Frequency | Cumulative Frequency |
|--------------|------------------|-----------|-----------|--------------------|----------------------|
| 26 - 36.2 | 25.95 - 36.25 | 31.1 | 4 | 0.05 | 4 |
| 36.3 - 46.4 | 36.25 - 46.45 | 41.35 | 21 | 0.26 | 25 |
| 46.5 - 56.6 | 46.45 - 56.65 | 51.55 | 45 | 0.56 | 70 |
| 56.7 - 66.8 | 56.65 - 66.85 | 61.75 | 7 | 0.09 | 77 |
| 66.9 - 77 | 66.85 - 77.05 | 71.95 | 3 | 0.04 | 80 |
```

This table summarizes the frequency distribution for the given data.

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