Question

find the median, first quartile (q1) and the third quartile (q3) for the data shown, which is already sorted. the number of data is n= 10. do not round your answers.
x
3.8
9.5
17.1
17.4
19.7
23.9
25.9
26.4
26.5
29.8
median =
q1 =
q3 =
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Explanation:

Step1: Find the median

For \( n = 10 \) (even number of data points), the median is the average of the \( \frac{n}{2} \)-th and \( (\frac{n}{2}+1) \)-th values.
\( \frac{n}{2}=5 \), so we take the 5th and 6th values. The 5th value is \( 19.7 \), the 6th value is \( 23.9 \).
Median \(=\frac{19.7 + 23.9}{2}=\frac{43.6}{2}=21.8\)

Step2: Find \( Q_1 \) (first quartile)

\( Q_1 \) is the median of the first half of the data. The first half has \( n_1 = 5 \) data points (values 1 to 5: \( 3.8, 9.5, 17.1, 17.4, 19.7 \)). For \( n_1 = 5 \) (odd), the median is the 3rd value. So \( Q_1 = 17.1 \)

Step3: Find \( Q_3 \) (third quartile)

\( Q_3 \) is the median of the second half of the data. The second half has \( n_2 = 5 \) data points (values 6 to 10: \( 23.9, 25.9, 26.4, 26.5, 29.8 \)). For \( n_2 = 5 \) (odd), the median is the 3rd value. So \( Q_3 = 26.4 \)

Answer:

Median = \( 21.8 \)
\( Q_1 = 17.1 \)
\( Q_3 = 26.4 \)