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
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To calculate the lower quartile, upper quartile, and interquartile range, you need to understand quartiles and how to find them in a dataset.
First, you need to arrange the data in ascending order: 20, 22, 25, 28, 29, 30, 32, 33, 34.
The lower quartile (Q1) is the median of the lower half of the dataset. To find it, you need to find the median of the first half of the data. In this case, the first half of the data is 20, 22, 25, and 28.
To find Q1:
1. Arrange the data in ascending order: 20, 22, 25, 28.
2. Since there is an even number of values, the median is the average of the two middle values: (22 + 25) / 2 = 23.5.
So, the lower quartile (Q1) is 23.5.
The upper quartile (Q3) is the median of the upper half of the dataset. To find it, you need to find the median of the second half of the data. In this case, the second half of the data is 30, 32, 33, and 34.
To find Q3:
1. Arrange the data in ascending order: 30, 32, 33, 34.
2. Since there is an even number of values, the median is the average of the two middle values: (32 + 33) / 2 = 32.5.
So, the upper quartile (Q3) is 32.5.
The interquartile range (IQR) is the difference between the upper quartile (Q3) and lower quartile (Q1). In this case, it is: 32.5 - 23.5 = 9.
Therefore, the lower quartile (Q1) is 23.5, the upper quartile (Q3) is 32.5, and the interquartile range (IQR) is 9.