Range: The range is the difference between the maximum and minimum values in a dataset.
To calculate the range:
Maximum value = 25
Minimum value = 4
Range = Maximum value - Minimum value =
25 - 4 = 21
Therefore, the range of the data is 21.
Interquartile range (IQR): The interquartile range is a measure of the spread of the data that focuses on the middle 50% of the dataset. It is calculated by subtracting the first quartile (Q1) from the third quartile (Q3).
To calculate the interquartile range:
First, we need to order the data from least to greatest: 4, 15, 17, 18, 20, 21, 23, 25
The median is the middle value, which is the average of the two middle values in this
case: (18 + 20) / 2 = 19
Q1 is the median of the lower half of the data, which is the middle value of the first
half: (15 + 17) / 2 = 16
Q3 is the median of the upper half of the data, which is the middle value of the
second half: (21 + 23) / 2 = 22
To calculate the interquartile range:
IQR = Q3 - Q1 = 22 - 16 = 6
Therefore, the interquartile range of the data is 6.
Now, let's describe how the data vary using the range and interquartile range:
The range of 21 shows that the data vary quite a bit, with the maximum value being 21 units greater than the minimum value.
The interquartile range of 6 indicates that the middle 50% of the data is relatively tightly clustered, with the spread between the first and third quartiles being 6 units.
Overall, the data exhibit a wide range of values, but the bulk of the data is relatively close together.