Using a class width of 1.425, construct a histogram with four bars:
1. Bar 1: 16.9 - 18.3 with a height of 2.
2. Bar 2: 18.4 - 19.8 with a height of 7.
3. Bar 3: 19.9 - 21.3 with a height of 1.
4. Bar 4: 21.4 - 22.8 with a height of 2.
To construct a histogram with 4 bars based on the given data, you can follow these steps:
1. **Determine the Range:**
Find the range of the data, which is the difference between the maximum and minimum values. In this case, the minimum value is 16.9 and the maximum value is 22.6. So, the range is \(22.6 - 16.9 = 5.7\).
2. **Determine the Class Width:**
Divide the range by the number of desired bars (in this case, 4) to determine the class width.
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3. **Determine the Lower Class Limits:**
Start with the minimum value in the data set and add the class width successively to determine the lower class limits for each bar.
- Bar 1: \(16.9\) - \(18.3\)
- Bar 2: \(18.4\) - \(19.8\)
- Bar 3: \(19.9\) - \(21.3\)
- Bar 4: \(21.4\) - \(22.8\)
4. **Construct the Histogram:**
Use the frequency information to determine the height of each bar. Each bar represents a class interval, and its height corresponds to the frequency of data points within that interval.
For example:
- Bar 1: Draw a bar from \(16.9\) to \(18.3\) on the x-axis with a height of 2.
- Bar 2: Draw a bar from \(18.4\) to \(19.8\) on the x-axis with a height of 7.
- Bar 3: Draw a bar from \(19.9\) to \(21.3\) on the x-axis with a height of 1.
- Bar 4: Draw a bar from \(21.4\) to \(22.8\) on the x-axis with a height of 2.
Mark each bar with black dots on the x-axis at the midpoint of the corresponding class interval.