Part 1

Given:

- Minimum = 12

- Maximum = 79

- Number of classes = 6

Step-by-Step Solution:

1. Calculate the Range:

\[\text { Range} = \text { Maximum} - \text { Minimum} = 79 - 12 = 67\]

2. Calculate the Class Width:

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

Since we want the class width as a whole number, we round up:

\[\text { Class Width} = \left \lceil \frac { 67} { 6} \right \rceil = \left \lceil 11.1667 \right \rceil = 12\]

3. Determine the Lower Class Limits:

Starting from the minimum value and adding the class width sequentially:

\[\begin{align*} \text { First class lower limit} &= 12 \\ \text { Second class lower limit} &= 12 + 12 = 24 \\ \text { Third class lower limit} &= 24 + 12 = 36 \\ \text { Fourth class lower limit} &= 36 + 12 = 48 \\ \text { Fifth class lower limit} &= 48 + 12 = 60 \\ \text { Sixth class lower limit} &= 60 + 12 = 72 \\ \end{align*} \]

4. Determine the Upper Class Limits:

The upper class limit is just below the next lower class limit:

\[\begin{align*} \text { First class upper limit} &= 23 \\ \text { Second class upper limit} &= 35 \\ \text { Third class upper limit} &= 47 \\ \text { Fourth class upper limit} &= 59 \\ \text { Fifth class upper limit} &= 71 \\ \text { Sixth class upper limit} &= 83 \\ \end{align*} \]

Therefore:

- The class width is 12.

- The correct lower class limits are: C. 12, 24, 36, 48, 60, 72

- The correct upper class limits are: D. 24, 36, 48, 60, 72, 83

Part 2

Given:

- Minimum = 8

- Maximum = 72

- Number of classes = 6

Step-by-Step Solution:

1. Calculate the Range:

\[\text { Range} = \text { Maximum} - \text { Minimum} = 72 - 8 = 64\]

2. Calculate the Class Width:

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

Since we want the class width as a whole number, we round up:

\[\text { Class Width} = \left \lceil \frac { 64} { 6} \right \rceil = \left \lceil 10.6667 \right \rceil = 11\]

3. Determine the Lower Class Limits:

Starting from the minimum value and adding the class width sequentially:

\[\begin{align*} \text { First class lower limit} &= 8 \\ \text { Second class lower limit} &= 8 + 11 = 19 \\ \text { Third class lower limit} &= 19 + 11 = 30 \\ \text { Fourth class lower limit} &= 30 + 11 = 41 \\ \text { Fifth class lower limit} &= 41 + 11 = 52 \\ \text { Sixth class lower limit} &= 52 + 11 = 63 \\ \end{align*} \]

4. Determine the Upper Class Limits:

The upper class limit is just below the next lower class limit:

\[\begin{align*} \text { First class upper limit} &= 18 \\ \text { Second class upper limit} &= 29 \\ \text { Third class upper limit} &= 40 \\ \text { Fourth class upper limit} &= 51 \\ \text { Fifth class upper limit} &= 62 \\ \text { Sixth class upper limit} &= 73 \\ \end{align*} \]

Therefore:

- The class width is 11.

- The correct lower class limits are: D. 8, 19, 30, 41, 52, 63

- The correct upper class limits are: B. 18, 29, 40, 51, 62, 73

Part 3

Given:

- Minimum = 15

- Maximum = 95

- Number of classes = 8

Step-by-Step Solution:

1. Calculate the Range:

\[\text { Range} = \text { Maximum} - \text { Minimum} = 95 - 15 = 80\]

2. Calculate the Class Width:

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

Since we want the class width as a whole number, we round up:

\[\text { Class Width} = \left \lceil \frac { 80} { 8} \right \rceil = \left \lceil 10 \right \rceil = 10\]

3. Determine the Lower Class Limits:

Starting from the minimum value and adding the class width sequentially:

\[\begin{align*} \text { First class lower limit} &= 15 \\ \text { Second class lower limit} &= 15 + 10 = 25 \\ \text { Third class lower limit} &= 25 + 10 = 35 \\ \text { Fourth class lower limit} &= 35 + 10 = 45 \\ \text { Fifth class lower limit} &= 45 + 10 = 55 \\ \text { Sixth class lower limit} &= 55 + 10 = 65 \\ \text { Seventh class lower limit} &= 65 + 10 = 75 \\ \text { Eighth class lower limit} &= 75 + 10 = 85 \\ \end{align*} \]

4. Determine the Upper Class Limits:

The upper class limit is just below the next lower class limit:

\[\begin{align*} \text { First class upper limit} &= 24 \\ \text { Second class upper limit} &= 34 \\ \text { Third class upper limit} &= 44 \\ \text { Fourth class upper limit} &= 54 \\ \text { Fifth class upper limit} &= 64 \\ \text { Sixth class upper limit} &= 74 \\ \text { Seventh class upper limit} &= 84 \\ \text { Eighth class upper limit} &= 94 \\ \end{align*} \]

Therefore:

- The class width is 10.

- The correct lower class limits are: B. 15, 25, 35, 45, 55, 65, 75, 85

- The correct upper class limits are: B. 24, 34, 44, 54, 64, 74, 84, 94

Additional Knowledge

Class Width Calculation:

- The class width determines the interval size for each class in a frequency distribution. It is crucial for creating histograms and other visual data representations.

Choosing Class Limits:

- Lower class limits start at the minimum value.

- Upper class limits are typically one less than the next lower class limit in a whole number system, ensuring there is no overlap.

Importance of Classes:

- Proper class intervals ensure that data is evenly distributed across classes, making the data easier to analyze and interpret.