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Answer :
Final answer:
To find the lower quartile, sort the data in ascending order, find the median, and then find the average of the two middle values in the lower half of the data.
Explanation:
To find the lower quartile, which represents the 25th percentile of the data, we need to first find the median, or the middle value. Sorting the data in ascending order, we get: {24.6, 38.8, 47.8, 49.6, 57, 57.6, 58.8, 65.4, 67.2}. The median is the middle value, which is 57.
Next, we divide the data into two halves. The lower half consists of {24.6, 38.8, 47.8, 49.6}.
Since there is an even number of values in the lower half, we take the average of the two middle values to find the lower quartile: (38.8 + 47.8) / 2 = 43.3.
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