Question
The data set represents the total number of tuba players in each of 11 difierent school bands. \( 0,1,3,3,4,4,4,5,6,6,8 \) What is the lower quartile of the data? 1 3 4 6 6
Ask by Crawford Parry.
Mar 14,2025 19:22
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Answer
The lower quartile of the data is 3.
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To find the lower quartile (Q1) of the data, we first need to arrange the numbers in ascending order, which they already are: \( 0, 1, 3, 3, 4, 4, 4, 5, 6, 6, 8 \). Since there are 11 data points, the lower quartile is located at the 25th percentile, which is the value at the \( \frac{1}{4}(n + 1) \) position. Here, \( n = 11 \), so \( Q1 \) is the value at position \( 3 \) (rounding down from 3.0).
Looking at the ordered set, the third value is \( 3 \), so the lower quartile is \( 3 \).
Now, the answer options provided would eliminate \( 3 \) as an answer if you look directly at the final options versus the calculated placement. However, from statistical calculation, the lower quartile is indeed \( 3 \).
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