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 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. The range is 14, and the interquartile range is 74.5. 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 8.
can you explain
Sure!
The range of a dataset is calculated by finding the difference between the maximum and minimum values. In this case, the highest height is 82 inches and the lowest height is 68 inches. So, the range is 82 - 68 = 14.
The interquartile range (IQR) is a measure of statistical dispersion, or how spread out the data is. It is calculated by finding the difference between the upper quartile (Q3) and the lower quartile (Q1) of the dataset.
To find the quartiles in this dataset:
1. Arrange the heights in ascending order: 68, 70, 74, 75, 78, 82.
2. Calculate the median:
- If the number of data points is odd, the median is the middle value. In this case, the median is 74.
- If the number of data points is even, the median is the average of the two middle values.
In this case, the median is 74.
3. Calculate Q1 (the median of the lower half of the data):
- In this dataset, the lower half is 68, 70, 74. The median of this lower half is 70.
4. Calculate Q3 (the median of the upper half of the data):
- In this dataset, the upper half is 75, 78, 82. The median of this upper half is 78.
Now, we can find the interquartile range:
IQR = Q3 - Q1
= 78 - 70
= 8.
Therefore, the range of the dataset is 14 inches, and the interquartile range is 8 inches.