Question

What is the mean, median, mode, and range of 2, 3, 3, 3, 3, 4, 4, 5, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 9?

Answer 1

Range `=7`
Median = `6`
Modes =`3,6,8`
Mean = `5.58`

Explanation:

`2,3,3,3,3,4,4,5,6,6,6,6,7,7,8,8,8,8,9`

Count the number of values first: There are `19`

Range: Difference between highest and lowest values:
#color(blue)(2),3,3,3,3,4,4,5,6,6,6,6,7,7,8,8,8,8, color(blue)(9)#

Range =`color(blue)(9-2 =7)`

Median: Value exactly in the middle of a set of data arranged in order. There are `19` values so this one is easy to find. It will be the `(19+1)/2 th` value = `10th`
`19 = 9+1+9`

`color(red)(2,3,3,3,3,4,4,5,6),6,color(red)(6,6,7,7,8,8,8,8,9)`
`color(white)(wwwwwwwwwwww)uarr`
`color(white)(wwwwwwwwwww)median =6`

Median: the value with the highest frequency - the one that occurs the MOST often:

`2,color(lime)(3,3,3,3),4,4,5,color(lime)(6,6,6,6),7,7,color(lime)(8,8,8,8),9`

There are three values which each occur `4` times
This is a tri-modal distribution, the modes are `3,6 and 8`

Mean: what is usually called the average. If all the values were the same, what would it be? Find one value to represent them all.

Mean: add all the values together and divide by `19`

`2+3+3+3+3+4+4+5+6+6+6+6+7+7+8+8+8+8+9 = 106`

`mean = color(magenta)(106/19 = 5.5789... ~~ 5.58)`