Question - Calculating Quartiles in a Data Set
Solution:
To find the lower quartile, median, and upper quartile of a data set, we'll follow these steps:1. **Median**: The median is the middle value of a data set when it's ordered from least to greatest. If the number of data points is odd, the median is the middle number. If it's even, the median is the average of the two middle numbers. For this set, there is an odd number of data points (7), so the median is the value in the middle - the fourth data point: $$ \text{Median} = 35 $$2. **Lower Quartile (Q1)**: The lower quartile is the median of the lower half of the data set (not including the median if the number of data points is odd). In this case, it's the median of the first three numbers: $$ \text{Lower quartile} = 26 $$ (as it is the middle of the first three numbers: 10, 26, 35)3. **Upper Quartile (Q3)**: The upper quartile is the median of the upper half of the data set (again, not including the median if the number of data points is odd). The upper half of this data set is the last three numbers: $$ \text{Upper quartile} = 55 $$ (as it is the middle of the last three numbers: 43, 55, 73)To summarize:- **Lower Quartile**: 26- **Median**: 35- **Upper Quartile**: 55
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