Question

what is the median of this data set?
24, 28, 51, 54, 67, 70
a. 51
b. 54
c. 52.5
d. 53.5

Explanation:

Step1: Count the number of data points

There are \(n = 6\) data points (\(24,28,51,54,67,70\)).

Step2: Use the median formula for even - numbered data sets

For \(n\) even, the median \(M=\frac{x_{\frac{n}{2}}+x_{\frac{n}{2}+1}}{2}\). Here, \(\frac{n}{2}=\frac{6}{2} = 3\) and \(\frac{n}{2}+1=4\).
\(x_3 = 51\) and \(x_4 = 54\).

Step3: Calculate the median

\(M=\frac{51 + 54}{2}=\frac{105}{2}=52.5\)

Answer:

C. 52.5