Question
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.
70, 78, 74, 82, 68, 75
Find the range and the interquartile range of the dataset.
Answers
To find the range, we subtract the smallest value from the largest value:
Range = 82 - 68 = 14
To find the interquartile range (IQR), we first need to find the median (middle value) of the dataset. To do this, we can order the numbers from smallest to largest:
68, 70, 74, 75, 78, 82
The median is the middle number, which is 75.
Next, we need to find the median of the lower half of the dataset (the values below the median). These are:
68, 70, 74
The median of these values is 70.
Similarly, we need to find the median of the upper half of the dataset (the values above the median). These are:
78, 82, 75
The median of these values is 77.5.
The interquartile range is the difference between the upper and lower quartiles, which is:
IQR = upper quartile - lower quartile
IQR = 77.5 - 70
IQR = 7.5
Therefore, the range of the dataset is 14 and the interquartile range is 7.5.
Range = 82 - 68 = 14
To find the interquartile range (IQR), we first need to find the median (middle value) of the dataset. To do this, we can order the numbers from smallest to largest:
68, 70, 74, 75, 78, 82
The median is the middle number, which is 75.
Next, we need to find the median of the lower half of the dataset (the values below the median). These are:
68, 70, 74
The median of these values is 70.
Similarly, we need to find the median of the upper half of the dataset (the values above the median). These are:
78, 82, 75
The median of these values is 77.5.
The interquartile range is the difference between the upper and lower quartiles, which is:
IQR = upper quartile - lower quartile
IQR = 77.5 - 70
IQR = 7.5
Therefore, the range of the dataset is 14 and the interquartile range is 7.5.