# What is the mean, median, mode, and range for the following numbers?: {4, 5, 1, 7, 6, 5, 3, 5, 4, 5, 3}

Oct 19, 2015

mean $= 4 \frac{4}{11}$
median $= 5$
mode $= 5$
range $= \left[1 , 7\right]$

#### Explanation:

mean is the numeric average: $\left(\text{sum of terms")/("number of terms}\right)$

mean $= \frac{4 + 5 + 1 + 7 + 6 + 5 + 3 + 5 + 4 + 5 + 3}{11} = \frac{48}{11} = 4 \frac{4}{11}$

median is the middle value when the data is arranged in numeric sequence (or the average of the two middle terms if there are an even number of terms)

Arranged in numeric sequence, the data become:
$< 1 , 3 , 3 , 4 , 4 , 5 , 5 , 5 , 5 , 6 , 7 >$
Splitting this sequence with an equal number of terms on each side and the "median" in the middle:
$< 1 , 3 , 3 , 4 , 4 > | | < 5 > | | < 5 , 5 , 5 , 6 , 7 >$

median = $5$

mode is the most commonly occurring term value
{: ("value", ,1, 3,4,5,6,7), ("number of occurrences",,1, 2,2,4,1,1) :}

mode = $5$

range is the upper and lower term values expressed as a pair
In this case the range is $\left[1 , 7\right]$