Question

What is the mode, median and mean of 5, 27, 29, 13, 18, 19, 15, 19, 19, 27, 15, 22, 13, 26, 20?

Answer 1

Mean `= 19.133`
Median `= 19`
Mode `= 19`

Explanation:

The Mean is the arithmetic average, `19.133`

The Median is `"([the number of data points] + 1) ÷ 2"`

or the PLACE value equidistant (numerically) from the range extremes in an ordered set.
This set contains `15` numbers, arranged in order as `5,13,13,15,15,18,19,19,19,20,22,26,27,27,29`.

So the middle place is `(15+1)/2 = 8th` position.
The number at that location is 19.

The Mode is the most common value(s) in a set. In this case it is `19`, with three occurrences in the set.

The closeness of all three of these measures means that the data is 'normally distributed'.

Answer 2

Mode = `19`

Median = `19`

Mean = `19.13`

Explanation:

A good starting place is to arrange the given values in order:

`5" "13" "13" "15" "15" "18" "19" "19" "19" "20" "22" "26" "27" "27" "29`

If you were asked the range. (which is not done in this case), it is now a simple matter to find the difference between the biggest and smallest values:
`color(blue)(5)" "13" "13" "15" "15" "18" "19" "19" "19" "20" "22" "26" "27" "27" "color(blue)(29)`

Range = `color(blue)(29-5 = 24)`

The MODE is the value with the highest frequency, the one that occurs the MOST often.
Because the values are all in order, we can see that `19` occurs three times.

`5" "13" "13" "15" "15" "18" "color(red)(19" "19" "19)" "20" "22" "26" "27" "27" "29`

Mode = `color(red)(19)`

The MEDIAN is the value exactly in the middle of a set of values arranged in order:
There are `15` numbers.

`15/2 = 7 1/2`

`15 = 7+1+7`

So count `7` from each side and the number in the middle is the median:

`color(green)(5, 13, 13, 15, 15, 18, 19)" "color(magenta)(19)" "color(green)(19, 20, 22, 26, 27, 27, 29)`

To find the MEAN (better known as the "average")

Add all the values together and divide by how many there are:

`5+13+13+15+15+18+19+19+19+20+22+26+27+27+29= 287`

`"Mean" = 287/15 = 19.13`

Remember that the mode, median and mean are ALL types of averages, they just give different information.