3.) Construct a frequency and a relative frequency histograms using 5 classes: 12 45 67 88 98 76 56 45 44 34 34 36 56 67 56 45 45 34 98 76 56 46 45 34

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### Step-by-Step Guide: Constructing Frequency and Relative Frequency Histograms, and a Stemplot

#### Task 3: Construct a Frequency and a Relative Frequency Histogram using 5 Classes

Given Data:
```
12, 45, 67, 88, 98, 76, 56, 45, 44, 34,
34, 36, 56, 67, 56, 45, 45, 34, 98, 76,
56, 46, 45, 34
```

**Steps to Construct the Histograms:**

1. **Determine the Range and Class Width:**
   - Find the minimum and maximum values in the dataset.
   - Minimum Value: 12
   - Maximum Value: 98
   - Range = Maximum - Minimum = 98 - 12 = 86
   - Number of Classes: 5
   - Class Width = Range ÷ Number of Classes
   - Class Width = 86 ÷ 5 = 17.2 (round up to 18)

2. **Set Class Limits:**
   - Class 1: 12 - 29
   - Class 2: 30 - 47
   - Class 3: 48 - 65
   - Class 4: 66 - 83
   - Class 5: 84 - 101

3. **Tally the Frequencies:**
   - Class 1: 12 (1)
   - Class 2: 30, 34, 34, 34, 34, 36, 44, 45, 45, 45, 45, 45, 46 (13)
   - Class 3: 48, 56, 56, 56, 56, 56 (5)
   - Class 4: 67, 67, 76, 76 (4)
   - Class 5: 88, 98, 98 (3)

4. **Calculate Relative Frequencies:**
   - Total number of data points: 24
   - Relative Frequency = (Frequency of Class) / (Total Number of Data Points)
   - Class 1: 1/24 ≈ 0.042 (4.2%)
   - Class 2: 13/24 ≈ 0.542 (54
Transcribed Image Text:### Step-by-Step Guide: Constructing Frequency and Relative Frequency Histograms, and a Stemplot #### Task 3: Construct a Frequency and a Relative Frequency Histogram using 5 Classes Given Data: ``` 12, 45, 67, 88, 98, 76, 56, 45, 44, 34, 34, 36, 56, 67, 56, 45, 45, 34, 98, 76, 56, 46, 45, 34 ``` **Steps to Construct the Histograms:** 1. **Determine the Range and Class Width:** - Find the minimum and maximum values in the dataset. - Minimum Value: 12 - Maximum Value: 98 - Range = Maximum - Minimum = 98 - 12 = 86 - Number of Classes: 5 - Class Width = Range ÷ Number of Classes - Class Width = 86 ÷ 5 = 17.2 (round up to 18) 2. **Set Class Limits:** - Class 1: 12 - 29 - Class 2: 30 - 47 - Class 3: 48 - 65 - Class 4: 66 - 83 - Class 5: 84 - 101 3. **Tally the Frequencies:** - Class 1: 12 (1) - Class 2: 30, 34, 34, 34, 34, 36, 44, 45, 45, 45, 45, 45, 46 (13) - Class 3: 48, 56, 56, 56, 56, 56 (5) - Class 4: 67, 67, 76, 76 (4) - Class 5: 88, 98, 98 (3) 4. **Calculate Relative Frequencies:** - Total number of data points: 24 - Relative Frequency = (Frequency of Class) / (Total Number of Data Points) - Class 1: 1/24 ≈ 0.042 (4.2%) - Class 2: 13/24 ≈ 0.542 (54
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