# What are the minimum, first quartile, median, mean, third quartile, and maximum of the following data set?: 10, 4, 9, 13, 5, 11, 5, 3, 7, 5

Jul 28, 2018

Minimum: 3

First quartile: 5

Median: 6

Third quartile: 10

Maximum: 13

#### Explanation:

First, let's list the data out from smallest to largest:
$3 , 4 , 5 , 5 , 5 , 7 , 9 , 10 , 11 , 13$

The minimum is the lowest number in the data set.
Since we listed it out from smallest to largest, we know that the minimum is $3$.


The median is the middle number. Cancel out $4$ numbers from each side and we are left with $2$ numbers:
$\cancel{3} , \cancel{4} , \cancel{5} , \cancel{5} , 5 , 7 , \cancel{9} , \cancel{10} , \cancel{11} , \cancel{13}$

Find the average of the middle $2$ numbers $5$ and $7$ to find the median:
$\frac{5 + 7}{2} = \frac{12}{2} = 6$
Therefore, the median is $6$.


The first quartile (Q1) is the median of the lower half of data which lies at 25% of the data.
Let's look at the lower half of numbers:
$3 , 4 , 5 , 5 , 5$

Cancel out $2$ numbers from each side and we are left with the $Q 1$:
$\cancel{3} , \cancel{4} , 5 , \cancel{5} , \cancel{5}$
Therefore, the $Q 1$ is $5$.


The third quartile (Q3) is the median of the upper half of data which lies at 75% of the data.

Let's look at the upper half of numbers:
$7 , 9 , 10 , 11 , 13$

Again cancel out $2$ numbers from each side:
$\cancel{7} , \cancel{9} , 10 , \cancel{11} , \cancel{13}$

The $Q 3$ is $10$.


The maximum is the highest number in the data set; it is $13$.

Hope this helps!