Question

the following data represents the miles per gallon of a random sample of automobiles. round to at least 4 decimal places.

(a) find the median.

(b) find \\( \overline { x } \\).

(c) find the variance.

(d) find \\( s \\).

Explanation:

Step1: Sort the data

First, sort the data in ascending order: \(19,22,24,25,29,33,34,34,35,37,41,41,42,42,42\)

Step2: Find the median

Since \(n = 15\) (odd), the median is the \(\frac{n + 1}{2}\)th value. \(\frac{15+ 1}{2}=8\)th value. The \(8\)th value in the sorted list is \(34\)

Step3: Calculate the mean \(\bar{x}\)

\(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}=\frac{19+22+24+25+29+33+34+34+35+37+41+41+42+42+42}{15}=\frac{512}{15}\approx34.1333\)

Step4: Calculate the variance \(s^{2}\)

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\(s^{2}=\frac{929.189}{14}\approx66.3706\)

Step5: Calculate the standard deviation \(s\)

\(s=\sqrt{s^{2}}=\sqrt{66.3706}\approx8.1468\)

Answer:

(a) \(34\)
(b) \(34.1333\)
(c) \(66.3706\)
(d) \(8.1468\)