Directions: Show all appropriate work. Write formulas used before plugging in numbers; include correct notation on 
answers; indicate which answer is which when more than 1 thing is asked. Circle all final numerical answers.  
1. Following is data collected of test scores from a sample of students in Mrs. Mayer’s Math 180 class.   
67, 73, 64, 94, 87, 78, 56, 76, 88, 48, 79, 51, 28, 75, 84, 89, 75, 67, 77, 98, 80, 38, 53, 62 
a. Find an appropriate class width for making a frequency distribution with 6 classes. 
b. Make a relative frequency distribution using 6 classes & the width you found in part a. Be sure fill in all 
columns of the given table, round the last column to 1 decimal place in the %. (I gave you your 1st lower limit) 
Class Limits 
Class Boundaries 
Tally 
Frequency 
28 -     
Relative Frequency (give as a %) 
c. Construct a histogram using the frequency distribution from part (b).

### 1. Data Collected of Test Scores from Mrs. Mayer’s Class:

Given data### 1. Data Collected of Test Scores from Mrs. Mayer’s Class:

Given   
67, 73, 64, 94, 87, 78, 56, 76, 88, 48, 79, 51, 28, 75, 84, 89, 75, 67, 77, 98, 80, 38, 53, 62

#### a. Finding the Class Width

To calculate the class width, we use the formula:

\[
\text{Class Width} = \frac{\text{Range}}{\text{Number of Classes}}
\]

1. **Range**: The range is the difference between the highest and lowest values in the data set.

\[
\text{Range} = \text{Max} - \text{Min} = 98 - 28 = 70
\]

2. **Number of Classes**: We are asked to create 6 classes.

\[
\text{Class Width} = \frac{70}{6} \approx 11.67
\]

We round the class width to the nearest whole number. So the class width is **12**.

#### b. Creating a Relative Frequency Distribution with 6 Classes

We start the first class at the given lower limit of **28** and then add the class width of **12** for the next classes. The table structure is:

| Class Limits | Class Boundaries | Tally | Frequency | Relative Frequency (%) |
|--------------|------------------|-------|-----------|------------------------|
| 28 - 39      | 27.5 - 39.5      |       |           |                        |
| 40 - 51      | 39.5 - 51.5      |       |           |                        |
| 52 - 63      | 51.5 - 63.5      |       |           |                        |
| 64 - 75      | 63.5 - 75.5      |       |           |                        |
| 76 - 87      | 75.5 - 87.5      |       |           |                        |
| 88 - 99      | 87.5 - 99.5      |       |           |                        |

Now, we tally the data### 1. Data Collected of Test Scores from Mrs. Mayer’s Class:

Given   
67, 73, 64, 94, 87, 78, 56, 76, 88, 48, 79, 51, 28, 75, 84, 89, 75, 67, 77, 98, 80, 38, 53, 62

#### a. Finding the Class Width

To calculate the class width, we use the formula:

\[
\text{Class Width} = \frac{\text{Range}}{\text{Number of Classes}}
\]

1. **Range**: The range is the difference between the highest and lowest values in the data set.

\[
\text{Range} = \text{Max} - \text{Min} = 98 - 28 = 70
\]

2. **Number of Classes**: We are asked to create 6 classes.

\[
\text{Class Width} = \frac{70}{6} \approx 11.67
\]

We round the class width to the nearest whole number. So the class width is **12**.

#### b. Creating a Relative Frequency Distribution with 6 Classes

We start the first class at the given lower limit of **28** and then add the class width of **12** for the next classes. The table structure is:

| Class Limits | Class Boundaries | Tally | Frequency | Relative Frequency (%) |
|--------------|------------------|-------|-----------|------------------------|
| 28 - 39      | 27.5 - 39.5      |       |           |                        |
| 40 - 51      | 39.5 - 51.5      |       |           |                        |
| 52 - 63      | 51.5 - 63.5      |       |           |                        |
| 64 - 75      | 63.5 - 75.5      |       |           |                        |
| 76 - 87      | 75.5 - 87.5      |       |           |                        |
| 88 - 99      | 87.5 - 99.5      |       |           |                        |

Now, we tally the 

**Tallying the Data**:
- 28 - 39: 28, 38 (2)
- 40 - 51: 48, 51 (2)
- 52 - 63: 56, 53, 62 (3)
- 64 - 75: 67, 64, 73, 75, 75, 67 (6)
- 76 - 87: 78, 76, 84, 87, 79, 80, 77 (7)
- 88 - 99: 94, 88, 98, 89 (4)

**Filling in the table**:

| Class Limits | Class Boundaries | Tally        | Frequency | Relative Frequency (%) |
|--------------|------------------|--------------|-----------|------------------------|
| 28 - 39      | 27.5 - 39.5      | |||

Directions: Show all appropriate work. Write formulas used before plugging in numbers; include correct notation on answers; indicate which answer is which when more than 1 thing is asked. Circle all final numerical answers. 
1. Following is data collected of test scores from a sample of students in Mrs. Mayer’s Math 180 class.
67, 73, 64, 94, 87, 78, 56, 76, 88, 48, 79, 51, 28, 75, 84, 89, 75, 67, 77, 98, 80, 38, 53, 62

a. Find an appropriate class width for making a frequency distribution with 6 classes.
b. Make a relative frequency distribution using 6 classes & the width you found in part a. Be sure to fill in all columns of the given table, round the last column to 1 decimal place in the %.
c. Construct a histogram using the frequency distribution from part (b).

Learn how to create a frequency distribution and relative frequency table using test scores from Mrs. Mayer's Math 180 class. This problem includes finding class width, filling in a frequency table with 6 classes, and constructing a histogram. Suitable for high school students, Grades 9-12.

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