How do you find the mean, median and mode of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10?

Mar 3, 2017

$\overline{x} = 5.5$
$\text{median} = 5.5$
No mode.

Explanation:

Recall that the mean ($\overline{x}$) of a data set is the sum of its terms divided by the number of terms.

$\overline{x} = \frac{{\Sigma}_{1}^{n} {a}_{n}}{n} = \frac{1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10}{10}$

$\overline{x} = \frac{55}{10} = 5.5$

Recall that the median of a data set is the value at the middle (the median) of the data set. In order to find the median, the data set must be arranged from lowest to highest. Once it is, we cross out one at the end, one at the beginning, one at the end, one at the beginning, and so on until we find the middle value.

$\cancel{1} , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , \cancel{10}$
$\cancel{1} , \cancel{2} , 3 , 4 , 5 , 6 , 7 , 8 , \cancel{9} , \cancel{10}$
$\cancel{1} , \cancel{2} , \cancel{3} , 4 , 5 , 6 , 7 , \cancel{8} , \cancel{9} , \cancel{10}$
$\cancel{1} , \cancel{2} , \cancel{3} , \cancel{4} , 5 , 6 , \cancel{7} , \cancel{8} , \cancel{9} , \cancel{10}$

Since there are an even number of terms, the median will be between the two middle values. Take the average of the two:

$\text{median} = \frac{5 + 6}{2} = 5.5$

The mode of a data set is the element that appears most frequently. Since each element in this data set is unique and only appears one time, there is no mode.