Answer :
To construct a relative frequency histogram for the given heights of 30 adult males using five classes, follow these steps:
1. Identify the Data Range:
- The heights range from 67 inches (minimum) to 74 inches (maximum).
- The data range is calculated as: [tex]\( \text{range} = \text{max height} - \text{min height} = 74 - 67 = 7 \)[/tex].
2. Determine Class Width:
- Divide the data range by the number of classes (5) to calculate the class width.
- Class width = 2 (as derived from dividing 7 by 5 and rounding up to the nearest whole number).
3. Create Class Intervals:
- Start with the minimum height (67) and create class intervals of the determined width (2).
- The classes are:
- 67-68
- 69-70
- 71-72
- 73-74
- 75-76
4. Frequency Distribution:
- Count how many heights fall into each class interval:
- 67-68: 6 heights
- 69-70: 10 heights
- 71-72: 10 heights
- 73-74: 4 heights
- 75-76: 0 heights
5. Calculate Relative Frequencies:
- Relative frequency for each class is calculated by dividing the class frequency by the total number of data points (30).
- Relative Frequencies:
- 67-68: [tex]\( \frac{6}{30} = 0.2 \)[/tex]
- 69-70: [tex]\( \frac{10}{30} \approx 0.33 \)[/tex]
- 71-72: [tex]\( \frac{10}{30} \approx 0.33 \)[/tex]
- 73-74: [tex]\( \frac{4}{30} \approx 0.13 \)[/tex]
- 75-76: [tex]\( \frac{0}{30} = 0.0 \)[/tex]
6. Construct the Histogram:
- The histogram bars represent the relative frequencies for each class interval:
- 67-68: Height of 0.2
- 69-70: Height of approximately 0.33
- 71-72: Height of approximately 0.33
- 73-74: Height of approximately 0.13
- 75-76: Height of 0.0
Using these steps, you successfully prepare a relative frequency histogram for the data given. Each step involves considering the distribution and frequency of the data over the constructed classes.
1. Identify the Data Range:
- The heights range from 67 inches (minimum) to 74 inches (maximum).
- The data range is calculated as: [tex]\( \text{range} = \text{max height} - \text{min height} = 74 - 67 = 7 \)[/tex].
2. Determine Class Width:
- Divide the data range by the number of classes (5) to calculate the class width.
- Class width = 2 (as derived from dividing 7 by 5 and rounding up to the nearest whole number).
3. Create Class Intervals:
- Start with the minimum height (67) and create class intervals of the determined width (2).
- The classes are:
- 67-68
- 69-70
- 71-72
- 73-74
- 75-76
4. Frequency Distribution:
- Count how many heights fall into each class interval:
- 67-68: 6 heights
- 69-70: 10 heights
- 71-72: 10 heights
- 73-74: 4 heights
- 75-76: 0 heights
5. Calculate Relative Frequencies:
- Relative frequency for each class is calculated by dividing the class frequency by the total number of data points (30).
- Relative Frequencies:
- 67-68: [tex]\( \frac{6}{30} = 0.2 \)[/tex]
- 69-70: [tex]\( \frac{10}{30} \approx 0.33 \)[/tex]
- 71-72: [tex]\( \frac{10}{30} \approx 0.33 \)[/tex]
- 73-74: [tex]\( \frac{4}{30} \approx 0.13 \)[/tex]
- 75-76: [tex]\( \frac{0}{30} = 0.0 \)[/tex]
6. Construct the Histogram:
- The histogram bars represent the relative frequencies for each class interval:
- 67-68: Height of 0.2
- 69-70: Height of approximately 0.33
- 71-72: Height of approximately 0.33
- 73-74: Height of approximately 0.13
- 75-76: Height of 0.0
Using these steps, you successfully prepare a relative frequency histogram for the data given. Each step involves considering the distribution and frequency of the data over the constructed classes.
