Question

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

11, 11, 12, 13

mean < median
mean = median
mean > median

Answer 1

the mean is greater than the median

Answer 2

Answer: mean > median

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}=(11+11+12+13)/(4)\\\\\Rightarrow\ \text{Mean}=(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=
`((n)/(2)\ term+((n)/(2)+1)\ term)/(2)`

`(n)/(2)\ term=(4)/(2)\ term=2nd\ term=11`

`(n)/(2)+1\ term=(4)/(2)+1\ term=3rd\ term=12`

Median=
`(11+12)/(2)=(23)/(2)=11.5`

Since, 11.75>11.5

Therefore, mean > median