Determine the classes. a) Find the highest and lowest values. b) Find the range. c) Select the number of classes desired. d) Find the width by dividing the range by the number of classes and rounding up. e) Select the starting point (usually the lowest value or any convenient number less than the lowest value); add the width to get the lowest limits. f) Find the upper limits. g) Find the boundaries. Step 2: Tally the data. Step 3: Find the numerical frequencies from the tallies, and the cumulative frequencies. Example 2: The data shown are the number of grams per serving of 30 selected brands of cakes. Construct a frequency distribution using 5 classes. 32 47 51 41 46 30 46 38 34 34 52 48 48 38 43 41 21 24 25 29 33 45 51 32 32 27 23 23 34 35 Frequency Table Class limits Class boundaries Tally Frequency Total
The Correct Answer and Explanation is:
Step 1: Organize and analyze the data
The provided data set is:
32, 47, 51, 41, 46, 30, 46, 38, 34, 34, 52, 48, 48, 38, 43, 41, 21, 24, 25, 29, 33, 45, 51, 32, 32, 27, 23, 23, 34, 35
a) Find the highest and lowest values:
- Lowest value: 21
- Highest value: 52
b) Find the range:
Range is the difference between the highest and lowest values.
- Range = Highest value – Lowest value = 52 – 21 = 31
c) Select the number of classes:
We are instructed to use 5 classes.
d) Find the width:
To find the width, we divide the range by the number of classes and round up.
- Width = Range ÷ Number of classes = 31 ÷ 5 = 6.2. Rounding up gives us a width of 7.
e) Select the starting point:
The starting point should be the lowest value or any convenient number less than the lowest value. Here, we choose 21 as the starting point since it’s the lowest value.
f) Find the upper limits:
We will now add the width (7) to each starting point to determine the class limits. The classes will look like this:
- 21 – 27
- 28 – 34
- 35 – 41
- 42 – 48
- 49 – 55
g) Find the boundaries:
Class boundaries are the points halfway between the upper limit of one class and the lower limit of the next class.
- Class boundaries:
- 20.5 – 27.5
- 27.5 – 34.5
- 34.5 – 41.5
- 41.5 – 48.5
- 48.5 – 55.5
Step 2: Tally the data
Now, we tally the data based on the class limits:
- Class 21 – 27: 21, 24, 25, 27 (4 tallies)
- Class 28 – 34: 29, 32, 32, 33, 34, 34, 34 (7 tallies)
- Class 35 – 41: 35, 38, 38, 41, 41, 43 (6 tallies)
- Class 42 – 48: 46, 46, 45, 47, 48, 48 (6 tallies)
- Class 49 – 55: 51, 51, 52 (3 tallies)
Step 3: Numerical frequencies and cumulative frequencies
Frequency table:
| Class Limits | Tally | Frequency | Cumulative Frequency |
|---|---|---|---|
| 21 – 27 | |||
| 28 – 34 | |||
| 35 – 41 | |||
| 42 – 48 | |||
| 49 – 55 |
Total frequency: 26
Conclusion
The frequency distribution is complete, and the cumulative frequency shows the running total of the number of values that fall into or below each class.
