The following data consists of the weights, in pounds, of 30 adults:

[tex]
\[
\begin{array}{l}
195, 206, 100, 98, 150, 210, 195, 106, 195, 168 \\
180, 212, 104, 195, 100, 216, 195, 209, 112, 99 \\
206, 116, 195, 100, 142, 100, 135, 98, 160, 155
\end{array}
\]
[/tex]

Using the data, complete the accompanying cumulative frequency table and construct a cumulative frequency histogram on the grid below.

[tex]
\[
\begin{tabular}{|c|c|}
\hline
Interval & Frequency \\
\hline
$51-100$ & \\
\hline
$101-150$ & \\
\hline
$151-200$ & \\
\hline
$201-250$ & \\
\hline
\end{tabular}
\]
[/tex]

Alright, let's solve the problem step-by-step.

### Step 1: Organize the Data and Determine Frequency

We need to find out how many weights fall into each of the given intervals:

1. [tex]$ 51-100 $[/tex]
2. [tex]$ 101-150 $[/tex]
3. [tex]$ 151-200 $[/tex]
4. [tex]$ 201-250 $[/tex]

Let's count the numbers in each interval:

#### Interval [tex]$ 51-100 $[/tex]:
- Weights: 100, 98, 100, 98, 100, 99, 100
- Count: 7

#### Interval [tex]$ 101-150 $[/tex]:
- Weights: 106, 104, 112, 116, 142, 135
- Count: 6

#### Interval [tex]$ 151-200 $[/tex]:
- Weights: 195, 195, 195, 168, 180, 195, 195, 195, 160, 155
- Count: 10

#### Interval [tex]$ 201-250 $[/tex]:
- Weights: 206, 210, 212, 216, 209, 206
- Count: 6

### Step 2: Complete the Cumulative Frequency Table

Construct the cumulative frequency by summing up the frequencies from each interval progressively:

| Interval | Frequency | Cumulative Frequency |
|------------|-----------|----------------------|
| 51-100 | 7 | 7 |
| 101-150 | 6 | 7 + 6 = 13 |
| 151-200 | 10 | 13 + 10 = 23 |
| 201-250 | 6 | 23 + 6 = 29 |

The Cumulative Frequency Table is as follows:

| Interval | Frequency | Cumulative Frequency |
|------------|-----------|----------------------|
| 51-100 | 7 | 7 |
| 101-150 | 6 | 13 |
| 151-200 | 10 | 23 |
| 201-250 | 6 | 29 |

### Step 3: Construct the Histogram

To plot a cumulative frequency histogram, follow these steps:

1. Label your x-axis with the intervals.
2. Label your y-axis with the cumulative frequency values.
3. Draw a bar for each interval up to the cumulative frequency value.

The plot would look something like this:

```
| x
| xx
| x xxx
| xx xxx
| x xx xxx
| xx xx xxx
| x xx xx xxx
| xx xx xx xxx
|_______xx____xx____xx___xxx_______
51-100 101-150 151-200 201-250
```

Each bar's height is the cumulative frequency for its respective interval.

That completes our solution and histogram construction!