Find the Median, IQ, UQ, IQR
5,9,11,3,14,20,25
Meidan 11
LQ 5
UQ 20
IQR 15
Did I do this right
3, 5, 9, 11, 14, 20, 25
Agree
Yes, you have correctly identified the median, lower quartile (LQ), upper quartile (UQ), and interquartile range (IQR) for the given data set.
To find the median:
1. Arrange the data in ascending order: 3, 5, 9, 11, 14, 20, 25.
2. Since the data set has an odd number of values, the median is the middle value, which in this case is 11.
To find the lower quartile (LQ):
1. Determine the position of the LQ, which is 25% of the way through the data set.
2. Multiply the total number of data points (7) by 0.25, which equals 1.75.
3. Since 1.75 is not a whole number, take the average of the two values surrounding it (1 and 2).
4. The LQ is the value at position 1.75, which corresponds to the first value in the data set, which is 5.
To find the upper quartile (UQ):
1. Determine the position of the UQ, which is 75% of the way through the data set.
2. Multiply the total number of data points (7) by 0.75, which equals 5.25.
3. Since 5.25 is not a whole number, take the average of the two values surrounding it (5 and 6).
4. The UQ is the value at position 5.25, which corresponds to the fifth value in the data set, which is 20.
To find the interquartile range (IQR):
1. Subtract the LQ from the UQ: 20 - 5 = 15.
Therefore, based on the calculations above, the median is 11, the lower quartile is 5, the upper quartile is 20, and the interquartile range is 15.