
116	105	116	115	111	104	107	113	85	109
106	117	101	109	118	99	95	93	116	87
114	119	92	112	107	114	97	97	108	90
105	114	101	90	108	94	105	110	117	89
106	104	89	111	92	119	94	116	106	97 with the first bin being 85-89 and there being a total of 7 bins

To create a frequency distribution with the given data and a specified bin range, we first need to determine the width of each bin and then count the number of data points that fall within each bin.

### Step-by-Step Process

1. **Data List**: Combine all the numbers into a single dataset.
   \[
   \text{Data} = [116, 105, 116, 115, 111, 104, 107, 113, 85, 109, 106, 117, 101, 109, 118, 99, 95, 93, 116, 87, 114, 119, 92, 112, 107, 114, 97, 97, 108, 90, 105, 114, 101, 90, 108, 94, 105, 110, 117, 89, 106, 104, 89, 111, 92, 119, 94, 116, 106, 97]
   \]

2. **Range and Bin Width**: 
   - The minimum value in the dataset is 85, and the maximum value is 119.
   - With 7 bins and the first bin being 85-89, the bin width can be calculated:
     \[
     \text{Bin width} = \frac{\text{Max Value} - \text{Min Value}}{\text{Number of Bins}} \approx \frac{119 - 85}{7} \approx 4.86 \approx 5 \text{ (rounded up to the nearest whole number)}
     \]

3. **Bin Intervals**: 
   The bins will be:
   - Bin 1: 85 - 89
   - Bin 2: 90 - 94
   - Bin 3: 95 - 99
   - Bin 4: 100 - 104
   - Bin 5: 105 - 109
   - Bin 6: 110 - 114
   - Bin 7: 115 - 119

4. **Counting the Frequencies**:
   - Count how many data points fall into each bin.

Let's perform these calculations to determine the frequencies.The frequency distribution for the data across the 7 bins is as follows:

1. **85 - 89**: 4 data points
2. **90 - 94**: 7 data points
3. **95 - 99**: 5 data points
4. **100 - 104**: 4 data points
5. **105 - 109**: 12 data points
6. **110 - 114**: 8 data points
7. **115 - 119**: 10 data points

This shows how the data is distributed within the specified range of bins.

Would you like more details or have any questions? Here are some related questions you might consider:

1. How do you calculate the cumulative frequency from this distribution?
2. What is the relative frequency for each bin?
3. Can you plot a histogram for this data?
4. How do these frequencies help in understanding the data distribution?
5. What is the mean and standard deviation of this dataset?

**Tip:** Understanding the distribution of your data can help identify patterns, outliers, and the spread of your dataset.

116 105 116 115 111 104 107 113 85 109 106 117 101 109 118 99 95 93 116 87 114 119 92 112 107 114 97 97 108 90 105 114 101 90 108 94 105 110 117 89 106 104 89 111 92 119 94 116 106 97 with the first bin being 85-89 and there being a total of 7 bins

Learn how to create a frequency distribution for the dataset ranging from 85 to 119, divided into 7 bins. This step-by-step solution covers statistical concepts like bin width calculation, frequency counting, and data binning. Suitable for students in Grades 9-12.

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