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.
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.
To find the range of a dataset, you subtract the minimum value from the maximum value. Let's find the range of the given dataset:
1. Sort the dataset in ascending order: 68, 70, 74, 75, 78, 82.
2. The minimum value is 68 and the maximum value is 82.
3. Calculate the range: 82 - 68 = 14.
Therefore, the range of the dataset is 14.
To find the interquartile range (IQR) of a dataset, you need to find the difference between the first quartile (Q1) and the third quartile (Q3). Here is how to calculate the IQR:
1. Sort the dataset in ascending order: 68, 70, 74, 75, 78, 82.
2. Calculate the position of Q1 in the dataset: (n + 1) / 4 = (6 + 1) / 4 = 1.75. Since this is not a whole number, we interpolate: Q1 = average of the 1st and 2nd data points = (68 + 70) / 2 = 69.
3. Calculate the position of Q3 in the dataset: 3 * (n + 1) / 4 = 3 * (6 + 1) / 4 = 5.25. Again, we interpolate: Q3 = average of the 5th and 6th data points = (78 + 82) / 2 = 80.
4. Calculate the IQR: Q3 - Q1 = 80 - 69 = 11.
Therefore, the interquartile range (IQR) of the dataset is 11.