High School

Data: 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

Formula: [tex]\text{Me} = \frac{x_{(n/2)} + x_{(n/2 + 1)}}{2}[/tex]

Find the median using the formula above.

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:


  1. 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.



  2. 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].



  3. 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.



  4. 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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