Calculate Frequency Distribution from -6,4,3, -9,2,8

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You entered a number set X of {-6,4,3,-9,2,8}

From the 6 numbers you entered, we want to build the Frequency Distribution Table:

Ranked Data Calculation

Sort our number set in ascending order

and assign a ranking to each number:

Ranked Data Table

Number Set Value	-9	-6	2	3	4	8
Rank	1	2	3	4	5	6

Step 2: Using original number set, assign the rank value:

Since we have 6 numbers in our original number set, we assign ranks from lowest to highest (1 to 6)
Our original number set in unsorted order was -6,4,3,-9,2,8
Our respective ranked data set is 2,5,4,1,3,6

Root Mean Square Calculation

Root Mean Square  =	√A
	√N

where A = x₁² + x₂² + x₃² + x₄² + x₅² + x₆² and N = 6 number set items

Calculate A

A = -9² + -6² + 2² + 3² + 4² + 8²

A = 81 + 36 + 4 + 9 + 16 + 64

A = 210

Calculate Root Mean Square (RMS):

RMS  =	√210
	√6

RMS  =	14.491376746189
	2.4494897427832

RMS = 5.9160797830996

Central Tendency Calculation

Central tendency contains:
Mean, median, mode, harmonic mean,
geometric mean, mid-range, weighted-average:

Calculate Mean (Average) denoted as μ

μ  =	Sum of your number Set
	Total Numbers Entered

μ  =	ΣXi
	n

μ  =	-9 + -6 + 2 + 3 + 4 + 8
	6

μ  =	2
	6

μ = 0.33333333333333

Calculate the Median (Middle Value)
Since our number set contains 6 elements which is an even number, our median number is determined as follows:
Number Set = (n₁,n₂,n₃,n₄,n₅,n₆)
Median Number 1 = ½(n)
Median Number 1 = ½(6)
Median Number 1 = Number Set Entry 3

Median Number 2 = Median Number 1 + 1
Median Number 2 = Number Set Entry 3 + 1
Median Number 2 = Number Set Entry 4

For an even number set, we average the 2 median number entries:
Median = ½(n₃ + n₄)

Therefore, we sort our number set in ascending order and our median is the average of entry 3 and entry 4 of our number set highlighted in red:
(-9,-6,2,3,4,8)
Median = ½(2 + 3)
Median = ½(5)
Median = 2.5