Calculate the mean, median and mode for the following data:
$15, \; 17, \; 16, \; 7, \; 10, \; 12, \; 14, \; 16, \; 19, \; 12, \; 16$
The given terms are: $\;$ $15, \; 17, \; 16, \; 7, \; 10, \; 12, \; 14, \; 16, \; 19, \; 12, \; 16$
Arranging the given terms in ascending order of their magnitude, we have
$7, \; 10, \; 12, \; 12, \; 14, \; 15, \; 16, \; 16, \; 16, \; 17, \; 19$
Sum of all terms $= \Sigma x = 154$
Number of terms $= n = 11$ (Odd number of terms)
Arithmetic mean $= \dfrac{\Sigma x}{n} = \dfrac{154}{11} = 14$
$\because \;$ $n$ is odd, median $= \left(\dfrac{n + 1}{2}\right)^{th}$ term
$\therefore \;$ Median $= \left(\dfrac{11 + 1}{2}\right)^{th}$ term $= 6^{th}$ term $= 15$
Mode $=$ value that occurs most frequently $= 16$