Question

A total of 25 patients admitted to a hospital are tested for levels of blood sugar, (mg/dl) and the results obtained were as follows:

$\begin{array}{ccccc}87& 71& 83& 67& 85\\ 77& 69& 76& 65& 85\\ 85& 54& 70& 68& 80\\ 73& 78& 68& 85& 73\\ 81& 78& 81& 77& 75\end{array}$

Find mean, median and mode (mg/dl) of the above data.

Answer 1

Firstly, arrange the given table in ascending order, which is shown below.

$\begin{array}{ccccc}54& 69& 75& 78& 85\\ 65& 70& 76& 80& 85\\ 67& 71& 77& 81& 85\\ 68& 73& 77& 81& 85\\ 68& 73& 78& 83& 87\end{array}$

Here, number of observations, n = 25
Sum of the results = 1891
$\therefore$ Mean of the given data
$=\frac{1891}{25}=75.64$
Here, n = 25 which is odd.
So, we use the formula for median $=\left(\frac{n+1}{2}\right)$th observation
$median=\left(\frac{25+1}{2}\right)$th observation
=13th observation = 77
We know that, mode is the highest frequency of an observation.
In the given table, we see that maximum repeated number is 85.
Hence, mode of the given data is 85.