Use the given minimum and maximum data entries, and the number of classes, to find the class width, the lower class limits, and the upper class limits. minimum = 9, maximum = 96, 7 classes The class width is (Type a whole number.) Use the minimum as the first lower class limit, and then find the remaining lower class limits. The lower class limits are (Type a whole number. Use a comma to separate answers as needed.) The upper class limits are (Type a whole number. Use a comma to separate answers as needed.)
The correct answer and explanation is :
Let’s break down the solution step by step.
Given Data:
- Minimum value = 9
- Maximum value = 96
- Number of classes = 7
Step 1: Finding the Class Width
The class width is calculated by using the formula:
$$
\text{Class Width} = \frac{\text{Maximum Value} – \text{Minimum Value}}{\text{Number of Classes}}
$$
Substituting the given values:
$$
\text{Class Width} = \frac{96 – 9}{7} = \frac{87}{7} = 12.42857
$$
Since the class width needs to be a whole number, we round this value up to the nearest whole number:
$$
\text{Class Width} = 13
$$
Step 2: Finding the Lower Class Limits
The first lower class limit is the minimum value, which is 9. To find the remaining lower class limits, we simply add the class width (13) to the previous lower class limit:
- First lower class limit = 9
- Second lower class limit = 9 + 13 = 22
- Third lower class limit = 22 + 13 = 35
- Fourth lower class limit = 35 + 13 = 48
- Fifth lower class limit = 48 + 13 = 61
- Sixth lower class limit = 61 + 13 = 74
- Seventh lower class limit = 74 + 13 = 87
Thus, the lower class limits are: 9, 22, 35, 48, 61, 74, 87.
Step 3: Finding the Upper Class Limits
To find the upper class limits, we subtract 1 from the next lower class limit:
- First upper class limit = 22 – 1 = 21
- Second upper class limit = 35 – 1 = 34
- Third upper class limit = 48 – 1 = 47
- Fourth upper class limit = 61 – 1 = 60
- Fifth upper class limit = 74 – 1 = 73
- Sixth upper class limit = 87 – 1 = 86
- Seventh upper class limit = 96 (since the maximum value is 96)
Thus, the upper class limits are: 21, 34, 47, 60, 73, 86, 96.
Final Answer:
- Class Width = 13
- Lower Class Limits = 9, 22, 35, 48, 61, 74, 87
- Upper Class Limits = 21, 34, 47, 60, 73, 86, 96
Explanation:
The class width is the difference between the maximum and minimum values divided by the number of classes. Since the class width needs to be a whole number, we round up the result. Then, we create intervals by starting with the minimum value and adding the class width to find the lower class limits. The upper class limits are derived by subtracting 1 from the next lower class limit to ensure there is no overlap between classes.