Question

do not round your answers.

x
1.4
4
5.4
9.3
10.8
13.3
13.7
15
19
27
29.7
median =
q₁ =
q₃ =
check answer

Explanation:

Step1: Count the number of data points

There are 11 data points (n = 11), which is odd.

Step2: Find the median

For odd n, the median is the \(\frac{n + 1}{2}\)-th term. \(\frac{11+ 1}{2}=6\)-th term. The data is ordered: 1.4, 4, 5.4, 9.3, 10.8, 13.3, 13.7, 15, 19, 27, 29.7. The 6th term is 13.3. So median = 13.3.

Step3: Find \(Q_1\) (first quartile)

\(Q_1\) is the median of the lower half. The lower half is the first 5 terms: 1.4, 4, 5.4, 9.3, 10.8. n = 5 (odd), so median of lower half is \(\frac{5 + 1}{2}=3\)-rd term. The 3rd term is 5.4. So \(Q_1 = 5.4\).

Step4: Find \(Q_3\) (third quartile)

\(Q_3\) is the median of the upper half. The upper half is the last 5 terms: 13.7, 15, 19, 27, 29.7. n = 5 (odd), so median of upper half is \(\frac{5 + 1}{2}=3\)-rd term. The 3rd term is 19. So \(Q_3 = 19\).

Answer:

Median = 13.3, \(Q_1 = 5.4\), \(Q_3 = 19\)