Calculate the interquartile range of the following data: 17, 18, 18, 19, 20, 21, 21, 23, 25
To find the interquartile range, we first need to find the median of the data set.
Median:
Arrange the data in order from smallest to largest:
17, 18, 18, 19, 20, 21, 21, 23, 25
The median is the middle number. Since there are 9 numbers in the set, the middle number is the 5th number.
Median = 20
Next, we need to find the median of the lower half of the data set (the numbers below the median).
Lower Half:
17, 18, 18, 19
The median of the lower half is the middle number. Since there are 4 numbers in the lower half, the middle number is the 2nd number.
Median of Lower Half = 18
Finally, we need to find the median of the upper half of the data set (the numbers above the median).
Upper Half:
21, 21, 23, 25
The median of the upper half is the middle number. Since there are 4 numbers in the upper half, the middle number is the 2nd number.
Median of Upper Half = 22
Now we have the first quartile (Q1) as the median of the lower half and the third quartile (Q3) as the median of the upper half.
Q1 = 18
Q3 = 22
Finally, we can calculate the interquartile range (IQR) by subtracting Q1 from Q3.
IQR = Q3 - Q1
IQR = 22 - 18
IQR = 4
Therefore, the interquartile range of the given data set is 4.
To calculate the interquartile range, you need to find the first quartile (Q1) and the third quartile (Q3) of the data set. Here's how you can do that step-by-step:
Step 1: Arrange the data in ascending order:
17, 18, 18, 19, 20, 21, 21, 23, 25
Step 2: Find the median, which is the middle value of the data set. Since we have 9 data points, the median will be the value in the middle, which is the (9+1)/2 = 5th value:
Median = 20
Step 3: Now split the data set into two halves. For the first half, which contains values less than or equal to the median, find the median again. This will be the first quartile (Q1):
First half: 17, 18, 18, 19, 20
Q1 = Median of the first half = (18 + 19)/2 = 18.5
Step 4: For the second half, which contains values greater than or equal to the median, find the median again. This will be the third quartile (Q3):
Second half: 20, 21, 21, 23, 25
Q3 = Median of the second half = (21 + 23)/2 = 22
Step 5: Calculate the interquartile range (IQR) by subtracting the first quartile (Q1) from the third quartile (Q3):
IQR = Q3 - Q1 = 22 - 18.5 = 3.5
Therefore, the interquartile range of the given data set is 3.5.