find the IQR of the data set: 2, 4, 5, 6, 8, 9, 13, 14, 15, 18
A:8
B:18
C:9
D:11
median of the 10 numbers is 8.5
1st quartile is 5
3rd quartile is 14
IQR = 14-5 = 9
Why did the statistician become an acrobat?
Because they wanted to calculate the IQR from a new perspective!
To find the IQR (Interquartile Range) of a data set, we need to find the median of the data set and then find the median of both the lower half and the upper half of the data set.
Step 1: Arrange the data set in ascending order: 2, 4, 5, 6, 8, 9, 13, 14, 15, 18
Step 2: Find the median:
Since there are an even number of data points, the median is the average of the two middle numbers. In this case, the two middle numbers are 8 and 9. The median is (8 + 9) / 2 = 8.5.
Step 3: Find the median of the lower half of the data set:
The lower half of the data set is: 2, 4, 5, 6, 8. The median is the middle number, which is 5.
Step 4: Find the median of the upper half of the data set:
The upper half of the data set is: 9, 13, 14, 15, 18. The median is the middle number, which is 14.
Step 5: Calculate the IQR by subtracting the lower quartile (Q1) from the upper quartile (Q3):
IQR = Q3 - Q1 = 14 - 5 = 9.
Therefore, the IQR of the given data set is 9.
The correct answer is C: 9.
To find the IQR (Interquartile Range) of a data set, you first need to determine the first quartile (Q1) and the third quartile (Q3). The IQR is the difference between Q3 and Q1.
1. Start by sorting the data set in ascending order: 2, 4, 5, 6, 8, 9, 13, 14, 15, 18.
2. Calculate the median: The middle value is 8 since there are an even number of values. The first quartile (Q1) is the median of the lower half of the data set: 2, 4, 5, 6. Q1 = 4.
3. Calculate the third quartile (Q3): The third quartile (Q3) is the median of the upper half of the data set: 13, 14, 15, 18. Q3 = 14.
4. Calculate the IQR: IQR = Q3 - Q1 = 14 - 4 = 10.
So, the correct answer is D: 10.