Using the following set of data, calculate the lower quartile, the upper quartile, and the interquartile range.
20, 22, 25, 28, 29, 30, 32, 33, 34
Be sure to show your work for finding:
the lower quartile
the upper quartile
the interquartile range
Q2 is the median of the set: 29
Q1 is the median of the 1st half: 25
Q3 is the median of the 2nd half: 32
The IQ Range is Q3-Q1: 7
To find the lower quartile, upper quartile, and interquartile range, let's first understand what these terms mean.
The quartiles divide a dataset into four equal parts. The lower quartile, also known as the first quartile (Q1), is the median of the lower half of the data. The upper quartile, also known as the third quartile (Q3), is the median of the upper half of the data. The interquartile range (IQR) measures the spread of the middle 50% of the data, and it is calculated by subtracting the lower quartile from the upper quartile.
Now, let's find the lower quartile, upper quartile, and interquartile range.
Step 1: Sort the data in ascending order:
20, 22, 25, 28, 29, 30, 32, 33, 34
Step 2: Find the median (Q2), which is the middle value of the dataset:
Median = (29 + 30) / 2 = 29.5
Step 3: Split the data into two halves:
Lower half: 20, 22, 25, 28
Upper half: 30, 32, 33, 34
Step 4: Find the lower quartile (Q1), which is the median of the lower half:
Q1 = (22 + 25) / 2 = 23.5
Step 5: Find the upper quartile (Q3), which is the median of the upper half:
Q3 = (32 + 33) / 2 = 32.5
Step 6: Calculate the interquartile range (IQR) by subtracting Q1 from Q3:
IQR = Q3 - Q1 = 32.5 - 23.5 = 9
Therefore, the lower quartile is 23.5, the upper quartile is 32.5, and the interquartile range is 9.