To find the range and the interquartile range (IQR) of the dataset, let's follow these steps:
1. **Range Calculation:**
- The range is the difference between the maximum and minimum values in the dataset.
- Dataset: 70, 78, 74, 82, 68, 75
- Minimum value: 68
- Maximum value: 82
- Range = Max - Min = 82 - 68 = 14
2. **Interquartile Range (IQR) Calculation:**
- The IQR is the difference between the third quartile (Q3) and the first quartile (Q1).
- First, sort the dataset: 68, 70, 74, 75, 78, 82
- Find the quartiles:
- Q1 (first quartile) is the median of the first half of the data:
- First half: 68, 70, 74 (n = 3)
- Q1 = 70 (2nd value in the first half)
- Q3 (third quartile) is the median of the second half of the data:
- Second half: 75, 78, 82 (n = 3)
- Q3 = 78 (2nd value in the second half)
- IQR = Q3 - Q1 = 78 - 70 = 8
Based on the computations above, the range is 14, and the interquartile range is 8. Therefore, the correct answer is:
- The range is 14, and the interquartile range is 8.
The heights in inches of six basketball players at a local high school are given as a dataset. 70, 78, 74, 82, 68, 75 Find the range and the interquartile range of the dataset. (1 point) Responses The range is 5, and the interquartile range is 8. The range is 5, and the interquartile range is 8. The range is 14, and the interquartile range is 4.5. The range is 14, and the interquartile range is 4.5. The range is 14, and the interquartile range is 8. The range is 14, and the interquartile range is 8. The range is 14, and the interquartile range is 74.5.
1 answer
1 answer