Min = 12, Max = 88, 6 classes
Use the minimum and maximum data entries and the number of classes to find the class width, the lower class limits, and the upper class limits.
The Correct Answer And Eplanation is:
To determine the class width, lower class limits, and upper class limits from the given data:
- Minimum (Min) = 12
- Maximum (Max) = 88
- Number of classes = 6
✅ Step 1: Find the Class Width
Use the formula: Class Width=Max−MinNumber of Classes\text{Class Width} = \frac{\text{Max} – \text{Min}}{\text{Number of Classes}} =88−126=766≈12.67= \frac{88 – 12}{6} = \frac{76}{6} \approx 12.67
Always round up the class width to the next whole number (to ensure all data is included): Class Width=13\text{Class Width} = 13
✅ Step 2: Determine the Lower Class Limits
Start from the minimum value (12) and add the class width to get the next starting point:
- Class 1: 12
- Class 2: 12 + 13 = 25
- Class 3: 25 + 13 = 38
- Class 4: 38 + 13 = 51
- Class 5: 51 + 13 = 64
- Class 6: 64 + 13 = 77
✅ Lower Class Limits: 12, 25, 38, 51, 64, 77
✅ Step 3: Determine the Upper Class Limits
Subtract 1 from the next lower class limit or add 12 (since width is 13):
- Class 1: 12 + 12 = 24
- Class 2: 25 + 12 = 37
- Class 3: 38 + 12 = 50
- Class 4: 51 + 12 = 63
- Class 5: 64 + 12 = 76
- Class 6: 77 + 12 = 89
✅ Upper Class Limits: 24, 37, 50, 63, 76, 89
🔍 Explanation (300+ words)
In statistics, constructing a frequency distribution table is an essential step in organizing raw data. It helps summarize large datasets and display them in a meaningful, structured form. The first step involves calculating the class width, which determines the size of each interval or class. The class width must be large enough to include all data values from the minimum to the maximum value.
To find the class width, subtract the minimum value (12) from the maximum value (88) and divide the result by the number of classes (6). This results in approximately 12.67. However, we round up to the nearest whole number — in this case, 13 — because rounding down could exclude the maximum data value from the last class.
Next, we calculate the lower class limits, starting from the minimum value (12) and adding the class width successively. These lower bounds define the starting number of each class interval.
After determining the lower limits, the upper class limits are found by adding 12 to each lower limit (one less than the class width) or by subtracting 1 from the next class’s lower limit. This ensures there is no overlap between classes and that every possible value is accounted for.
These class limits define six intervals that fully cover the range from 12 to 88 without gaps or overlaps. This method is crucial when organizing data for histograms, frequency tables, or further statistical analysis such as mean, median, or standard devia