Question

2.5 measures of the center of the data
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the following data show the lengths of boats moored in a marina. the data are ordered from smallest to largest.
16, 17, 19, 20, 20, 21, 22, 23, 24, 24, 24, 25, 25, 26, 26, 26, 27, 28, 29, 32, 33, 33, 34, 35, 37, 39, 40
identify the median. (enter an exact number as an integer, fraction, or decimal.)
what position does the median have in an ordered list of numbers when the data set contains an odd number of items?
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Explanation:

Step1: Count the number of data points

There are \(n = 27\) data points.

Step2: Use the formula for the position of the median

The formula for the position of the median when \(n\) is odd is \(\frac{n + 1}{2}\). Substituting \(n=27\), we get \(\frac{27+ 1}{2}=\frac{28}{2}=14\).

Step3: Find the median

Since the data is ordered from smallest to largest, the median is the 14th - value in the ordered list. Counting the values: \(16\) (1), \(17\) (2), \(19\) (3), \(20\) (4), \(20\) (5), \(21\) (6), \(22\) (7), \(23\) (8), \(24\) (9), \(24\) (10), \(24\) (11), \(25\) (12), \(25\) (13), \(26\) (14).

Answer:

The median is \(26\) and the position of the median in an ordered list of numbers when the data - set contains an odd number of items is \(\frac{n + 1}{2}\) (where \(n\) is the number of data points).