In the data set below, what is the interquartile range? 41474950567297979798
To find the interquartile range, we first need to find the first and third quartiles.
1. Arrange the data in ascending order: 4, 4, 4, 5, 5, 5, 6, 7, 9, 7, 9, 9, 9, 7, 9, 8, 7, 9, 8
2. Find the median (middle value) of the data set. Since there are 19 numbers, the median will be the average of the 9th and 10th numbers:
Median = (7 + 9) / 2 = 8
3. Now we need to find the median of the lower half of the data set (numbers less than or equal to the overall median) to get the first quartile. In this case, the lower half is 4, 4, 4, 5, 5, 5, 6, 7, and 7:
Q1 = 5
4. To find the median of the upper half of the data set (numbers greater than or equal to the overall median), we get the third quartile. In this case, the upper half is 9, 9, 9, 9, 9, 8, 9, and 8:
Q3 = 9
5. Finally, calculate the interquartile range (IQR) by subtracting Q1 from Q3:
IQR = Q3 - Q1 = 9 - 5 = 4
Therefore, the interquartile range of the given data set is 4.