Question

Based on the following set of data, which of the statements shown is true?

Answer 1

The mean is greater than the median

Answer 2

Answer: mean > median

Step-by-step explanation:

The given data : 11, 11, 12, 13

The mean of the given data set is given by :-

$\text{Mean}=\frac{\text{Sum of all elements}}{\text{number of all elements}}\\\\\Rightarrow\ \text{Mean}=\frac{11+11+12+13}{4}\\\\\Rightarrow\ \text{Mean}=\frac{47}{4}\\\\\Rightarrow\ \text{Mean}=11.75$

To find median, first arrange them in ascending order  and since the number of elements is a even number(n=4), therefore,

Median=$\frac{\frac{n}{2}\ term+(\frac{n}{2}+1)\ term}{2}$

$\frac{n}{2}\ term=\frac{4}{2}\ term=2nd\ term=11$

$\frac{n}{2}+1\ term=\frac{4}{2}+1\ term=3rd\ term=12$

Median=$\frac{11+12}{2}=\frac{23}{2}=11.5$

Since, 11.75>11.5

Therefore, mean > median