Example 2.27 from Statistics, 2.5 Measures of the Center of the Data

Measures of the Center of the Data: example 2.27

Data indicating the number of months a patient with a specific disease lives after taking a new antibody drug are as follows (smallest to largest):
3, 4, 8, 8, 10, 11, 12, 13, 14, 15, 15, 16, 16, 17, 17, 18, 21, 22, 22, 24, 24, 25, 26, 26, 27, 27, 29, 29, 31, 32, 33, 33, 34, 34, 35, 37, 40, 44, 44, 47
Calculate the mean and the median.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
The calculation for the mean is

$\begin{array}{l} \bar{x} = [3 + 4 + (8) (2) + 10 + 11 + 12 + 13 + 14 + (15) (2) + (16) (2) + (17) (2) + 18 + 21 + (22) (2) + (24) (2) + 25 + (26) (2) \\ + (27) (2) + (29) (2) + 31 + 32 + (33) (2) + (34) (2) + 35 + 37 + 40 + (44) (2) + 47] / 40 = 23.6. \end{array}$
To find the median, M, first use the formula for the location. The location is
$\frac{n + 1}{2} = \frac{40 + 1}{2} = 20.5.$
Start from the smallest value and count up; the median is located between the 20^th and 21^st values (the two 24s):
3, 4, 8, 8, 10, 11, 12, 13, 14, 15, 15, 16, 16, 17, 17, 18, 21, 22, 22, 24, 24, 25, 26, 26, 27, 27, 29, 29, 31, 32, 33, 33, 34, 34, 35, 37, 40, 44, 44, 47
$M = \frac{24 + 24}{2} = 24$

How did it go?

Solution

Solution