William wishes to view a frequency table for grouped data using his monthly credit card statements for the last 20 months, shown below. Construct the table for William using six classes.  
1184,1247,945,1124,1034,1352,1025,1439,1136,1439,1368,1057,1130, 
1259,1256,1381,838,1342,842,1395
​
  Provide your answer below:

To create a frequency table for William's monthly credit card statements, we will follow these steps:

### Step 1: Organize the data
The given credit card statements over the last 20 months are:
\[ 1184, 1247, 945, 1124, 1034, 1352, 1025, 1439, 1136, 1439, 1368, 1057, 1130, 1259, 1256, 1381, 838, 1342, 842, 1395 \]

### Step 2: Determine the range
The range is the difference between the largest and smallest values.

- Largest value: \( 1439 \)
- Smallest value: \( 838 \)

\[
\text{Range} = 1439 - 838 = 601
\]

### Step 3: Calculate the class width
To find the class width, divide the range by the number of classes (6 in this case) and round up to the next whole number.

\[
\text{Class width} = \frac{601}{6} \approx 100.17 \Rightarrow 101
\]

### Step 4: Define the class intervals
Start with the smallest value \( 838 \) and create 6 classes, each with a width of 101.

The class intervals will be:
1. \( 838 - 938 \)
2. \( 939 - 1039 \)
3. \( 1040 - 1140 \)
4. \( 1141 - 1241 \)
5. \( 1242 - 1342 \)
6. \( 1343 - 1443 \)

### Step 5: Tally the data into the classes
Now, we tally the data values into the respective classes.

- **Class 1 (838 - 938)**: \( 838, 842 \)
- **Class 2 (939 - 1039)**: \( 945, 1034 \)
- **Class 3 (1040 - 1140)**: \( 1057, 1124, 1130, 1136 \)
- **Class 4 (1141 - 1241)**: \( 1184, 1247, 1256, 1259 \)
- **Class 5 (1242 - 1342)**: \( 1342, 1352 \)
- **Class 6 (1343 - 1443)**: \( 1368, 1381, 1395, 1439, 1439 \)

### Step 6: Create the frequency table

| Class Interval | Frequency |
|----------------|-----------|
| 838 - 938      | 2         |
| 939 - 1039     | 2         |
| 1040 - 1140    | 4         |
| 1141 - 1241    | 4         |
| 1242 - 1342    | 2         |
| 1343 - 1443    | 6         |

Thus, the frequency table for William’s credit card statements over the past 20 months is as shown above.

Would you like further clarification or details on how this table was constructed?

### Related Questions:
1. How would the table change if there were 8 classes instead of 6?
2. What would the cumulative frequency table look like for this data?
3. How could we compute the mean monthly spending using this grouped data?
4. What is the mode class in this frequency table?
5. How would a histogram look based on this frequency table?

**Tip**: Always round up the class width to ensure that all data points are covered within the intervals.

William wishes to view a frequency table for grouped data using his monthly credit card statements for the last 20 months, shown below. Construct the table for William using six classes. 1184, 1247, 945, 1124, 1034, 1352, 1025, 1439, 1136, 1439, 1368, 1057, 1130, 1259, 1256, 1381, 838, 1342, 842, 1395

Learn how to create a frequency table for grouped data using monthly credit card statements from the last 20 months. This solution includes step-by-step calculations for determining the range, class width, and constructing six classes. Ideal for high school students studying statistics and data analysis.

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