# How do you find the mean, median, mode and range of 30, 34, 35, 39, 33, 32, 31, 36, 35, 37?

Dec 20, 2016

See explanation.

#### Explanation:

First thing we need tio do is to put the data in increasing order. This is needed to calculate the median:

$30 , 31 , 32 , 33 , 34 , 35 , 35 , 36 , 37 , 39$

Now we can calculate the parameters of this set:

• Mean:

$\overline{x} = \frac{30 + 31 + 32 + 33 + 34 + 35 + 35 + 36 + 37 + 39}{10} = \frac{342}{10} = 34.2$

• Median

To calculate the median we need to take "middle" elements in an ordered set. If the set has an odd number of elements, then there is only one middle element, otherwise there are 2 such elements and median is the mean of those elements.

To find the middle elements we can cross out elements at both ends of the set until only 1 or 2 remain uncrossed:

$\cancel{30} , 31 , 32 , 33 , 34 , 35 , 35 , 36 , 37 , \cancel{39}$

$\cancel{30} , \cancel{31} , 32 , 33 , 34 , 35 , 35 , 36 , \cancel{37} , \cancel{39}$

$\cancel{30} , \cancel{31} , \cancel{32} , 33 , 34 , 35 , 35 , \cancel{36} , \cancel{37} , \cancel{39}$

$\cancel{30} , \cancel{31} , \cancel{32} , \cancel{33} , 34 , 35 , \cancel{35} , \cancel{36} , \cancel{37} , \cancel{39}$

There are 2 uncrossed elements, so their mean is the median: $M e = \frac{34 + 35}{2} = \frac{69}{2} = 34.5$

• Mode is the element which occurs the most times in the set. Here it is $35$.

• Range is the difference between the smallest and the largest element: $r = 39 - 30 = 9$