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Answer :
To find the median using the given formula [tex]Me = \frac{x_{n/2} + x_{n/2 + 1}}{2}[/tex], we need to follow these steps:
Identify the total number of data points:
- The data set provided is: 161, 163, 166, 166, 167, 167, 168, 168, 169, 170, 171, 172, 172, 172, 173, 173, 173, 174, 174, 175, 175, 176, 176, 176, 177, 177, 178, 180, 181, 183.
- There are 30 data points in total.
Determine [tex]n/2[/tex] and [tex]n/2 + 1[/tex]:
- Since [tex]n = 30[/tex], we calculate [tex]n/2[/tex] as [tex]30/2 = 15[/tex].
- Thus, [tex]n/2 + 1 = 15 + 1 = 16[/tex].
Identify the 15th and 16th data points in the ordered list:
- From the ordered data set, the 15th data point is 173 and the 16th data point is also 173.
Apply the formula to find the median:
[tex]Me = \frac{x_{15} + x_{16}}{2} = \frac{173 + 173}{2} = \frac{346}{2} = 173[/tex]
Therefore, the median of the data set is 173.
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