127 125 125 129 123 126 127 128 128 125. Find the range and the interquartile range of the data set
To find the range, subtract the minimum value from the maximum value in the data set:
Range = 129 - 123 = 6
To find the interquartile range, first we need to find the first and third quartiles. The first quartile (Q1) is the median of the data set to the left of the overall median, and the third quartile (Q3) is the median of the data set to the right of the overall median.
The data set in ascending order is: 123, 125, 125, 125, 126, 127, 127, 128, 128, 129
There are 10 numbers in the data set, so the median is the average of the 5th and 6th numbers:
(126 + 127) / 2 = 126.5
The first quartile is the median of the first half of the data set (123, 125, 125, 125, 126):
Q1 = (125 + 125) / 2 = 125
The third quartile is the median of the second half of the data set (127, 127, 128, 128, 129):
Q3 = (128 + 128) / 2 = 128
Interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1):
IQR = Q3 - Q1 = 128 - 125 = 3
So, the range of the data set is 6, and the interquartile range is 3.