Answer:
To find the range of a data set, we subtract the minimum value from the maximum value.
Given the data set: 47, 38, 72, 56, 40, 64, 30, 80, 66, 51
The minimum value is 30, and the maximum value is 80.
Range = Maximum value - Minimum value
= 80 - 30
= 50
Therefore, the range for the data set is 50.
To find the interquartile range (IQR), we need to determine the values of the first quartile (Q1) and the third quartile (Q3) and then calculate the difference between them.
First, we need to order the data set in ascending order:
30, 38, 40, 47, 51, 56, 64, 66, 72, 80
Q1 represents the 25th percentile.
Q3 represents the 75th percentile.
To find Q1, we take the average of the values at the 25th and 26th positions (since it falls between 38 and 40):
Q1 = (38 + 40) / 2
= 78 / 2
= 39
To find Q3, we take the average of the values at the 75th and 76th positions (since it falls between 66 and 72):
Q3 = (66 + 72) / 2
= 138 / 2
= 69
Now, we can calculate the interquartile range (IQR):
IQR = Q3 - Q1
= 69 - 39
= 30
Therefore, the interquartile range (IQR) for the given data set is 30.