Rainwater was collected at thirty different sites near an industrial basin and the amount of acidity (pH level) was measured. The pH values were:2.6, 2.7, 2.9, 3.2, 3.3, 3.7, 3.7, 3.8, 3.9, 4.1, 4.2, 4.2, 4.2, 4.4, 4.4,4.6, 4.8, 4.9, 4.9, 5.0, 5.5, 5.5, 5.6, 5.7, 5.8, 5.8, 6.0, 6.2 6.3, 6.3The interquartile range is:
Question
Rainwater was collected at thirty different sites near an industrial basin and the amount of acidity (pH level) was measured. The pH values were:2.6, 2.7, 2.9, 3.2, 3.3, 3.7, 3.7, 3.8, 3.9, 4.1, 4.2, 4.2, 4.2, 4.4, 4.4,4.6, 4.8, 4.9, 4.9, 5.0, 5.5, 5.5, 5.6, 5.7, 5.8, 5.8, 6.0, 6.2 6.3, 6.3The interquartile range is:
Solution
To calculate the interquartile range (IQR), we first need to find the values of the first quartile (Q1) and the third quartile (Q3).
Step 1: Arrange the data in ascending order, which has already been done in this case.
Step 2: Find the median of the data set. Since there are 30 data points, the median is the average of the 15th and 16th values. In this case, the median is (4.4 + 4.6) / 2 = 4.5.
Step 3: Find Q1, which is the median of the first half of the data. Since there are 15 data points in the first half, the median is the 8th value, which is 3.8.
Step 4: Find Q3, which is the median of the second half of the data. Since there are 15 data points in the second half, the median is the 8th value of the second half, which is 5.5.
Step 5: Calculate the IQR, which is Q3 - Q1. In this case, the IQR is 5.5 - 3.8 = 1.7.
So, the interquartile range of the pH values is 1.7.
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