You entered a number set X of {2,4,6,8,10}
Do 3 things
Run statistical calculations on this
Treat ths as a vector and run calculations on this
Treat this as a sequence

Order This Number Set

Order lowest to highest
2 < 4 < 6 < 8 < 10

Order highest to lowest
10 > 8 > 6 > 4 > 2

Basic Stats Calculations

Mean, Variance, Standard Deviation, Median, Mode

Calculate Mean (Average) denoted as μ

μ =	Sum of your number Set
	Total Numbers Entered

μ =	ΣX_i
	n

μ =	2 + 4 + 6 + 8 + 10
	5

μ =	30
	5

μ = 6

Calculate variance denoted as σ²

Evaluate the square difference from the mean of each term
(X_i - μ)²:

(X₁ - μ)² = (2 - μ = 6)² = 2² = 4
(X₂ - μ)² = (4 - μ = 6)² = 4² = 16
(X₃ - μ)² = (6 - μ = 6)² = 6² = 36
(X₄ - μ)² = (8 - μ = 6)² = 8² = 64
(X₅ - μ)² = (10 - μ = 6)² = 10² = 100

Add our 5 sum of squared differences up

ΣE(X_i - μ)² = 4 + 16 + 36 + 64 + 100
ΣE(X_i - μ)² = 220

Variance Table

Population

Sample

σ² =	ΣE(X_i - μ)²
	n

σ² =	ΣE(X_i - μ)²
	n - 1

σ² =	220
	5

σ² =	220
	4

Variance: σ_p² = 44

Variance: σ_s² = 55

Standard Deviation: σ_p = √σ_p² = √44

Standard Deviation: σ_s = √σ_s² = √55

Standard Deviation: σ_p = 6.6332

Standard Deviation: σ_s = 7.4162

Calculate the Standard Error of the Mean:

Population

Sample

SEM =	σ_p
	√n

SEM =	σ_s
	√n

SEM =	6.6332
	√5

SEM =	7.4162
	√5

SEM =	6.6332
	2.2360679774998

SEM =	7.4162
	2.2360679774998

SEM = 2.9665

SEM = 3.3166

Calculate Skewness:

Skewness =	E(X_i - μ)³
	(n - 1)σ³

Let's evaluate the square difference from the mean of each term (X_i - μ)³:
(X₁ - μ)³ = (2 - μ = 6)³ = 2³ = 8
(X₂ - μ)³ = (4 - μ = 6)³ = 4³ = 64
(X₃ - μ)³ = (6 - μ = 6)³ = 6³ = 216
(X₄ - μ)³ = (8 - μ = 6)³ = 8³ = 512
(X₅ - μ)³ = (10 - μ = 6)³ = 10³ = 1000

Adding our 5 sum of cubed differences

ΣE(X_i - μ)³ = 8 + 64 + 216 + 512 + 1000
ΣE(X_i - μ)³ = 1800

Finish calculating skewness:

Skewness =	E(X_i - μ)³
	(n - 1)σ³

Skewness =	1800
	(5 - 1)6.6332³

Skewness =	1800
	(4)291.85643694637

Skewness =	1800
	1167.4257477855

Skewness = 1.5418539495248

Calculate Average Deviation (Mean Absolute Deviation) denoted below:

AD =	Σ\|X_i - μ\|
	n

Let's evaluate the absolute value of the difference from the mean of each term |X_i - μ|:
|X₁ - μ| = |2 - μ = 6| = |2| = 2
|X₂ - μ| = |4 - μ = 6| = |4| = 4
|X₃ - μ| = |6 - μ = 6| = |6| = 6
|X₄ - μ| = |8 - μ = 6| = |8| = 8
|X₅ - μ| = |10 - μ = 6| = |10| = 10

Add our 5 absolute value of differences from the mean

Σ|X_i - μ| = 2 + 4 + 6 + 8 + 10
Σ|X_i - μ| = 30

Calculate average deviation (mean absolute deviation)

AD =	Σ\|X_i - μ\|
	n

AD =	30
	5

Average Deviation = 6

Calculate the Median (Middle Value)

Since our number set contains 5 elements which is an odd number
our median number is determined as follows:
Number Set = (n₁,n₂,n₃,n₄,n₅)
Median Number = Entry ½(n + 1)
Median Number = Entry ½(6)
Median Number = n₃

Final Median Calculation

Therefore, we sort our number set in ascending order and our median is
entry 3 of our number set highlighted in red:
(
2)
,4)
,6)
,8)
,10)
Median = 6

Calculate the Mode - Highest Frequency Number

The highest frequency of occurence in our number set is
1 times by the following numbers in green:
(2,4,6,8,10)
Since the maximum frequency of any number is 1, no mode exists.

Calculate the Range

Range = Largest Number - Smallest Number
Range = 10 - 2
Range = 8

Calculate Mid-Range:

Mid-Range =	Smallest Number in the Set + Largest Number in the Set
	2

Mid-Range =	10 + 2
	2

Mid-Range =	12
	2

Mid-Range = 6

Calculate Pearsons Skewness Coefficient 1:

PSC1 =	μ - Mode
	σ

PSC1 =	3( μ = 6 - N/A)
	6.6332

Since no mode exists, we do not have a Pearsons Skewness Coefficient 1

Calculate Pearsons Skewness Coefficient 2:

PSC2 =	μ - Median
	σ

PSC1 =	3( μ = 6 - 6)
	6.6332

PSC2 =	3 x -6
	6.6332

PSC2 =	-18
	6.6332

PSC2 = -2.7136

Calculate Entropy:

Entropy = Ln(n)
Entropy = Ln(5)
Entropy = 1.6094379124341

Calculate the Quartile Items

Sort our number set from lowest to highest
{2,4,6,8,10}

Calculate Upper Quartile (UQ) when y = 75%:

V =	y(n + 1)
	100

V =	75(5 + 1)
	100

V =	75(6)
	100

V =	450
	100

V = 4 ← Rounded down to the nearest integer

Upper quartile (UQ) point = Point # 4 in the dataset which is 8
2,4,6,8,10

Calculate Lower Quartile (LQ) when y = 25%:

V =	y(n + 1)
	100

V =	25(5 + 1)
	100

V =	25(6)
	100

V =	150
	100

V = 2 ← Rounded up to the nearest integer

Lower quartile (LQ) point = Point # 2 in the dataset which is 4

2,4,6,8,10

Calculate Inter-Quartile Range (IQR):

IQR = UQ - LQ
IQR = 8 - 4
IQR = 4

Calculate Lower Inner Fence (LIF):

Lower Inner Fence (LIF) = LQ - 1.5 x IQR
Lower Inner Fence (LIF) = 4 - 1.5 x 4
Lower Inner Fence (LIF) = 4 - 6
Lower Inner Fence (LIF) = -2

Calculate Upper Inner Fence (UIF):

Upper Inner Fence (UIF) = UQ + 1.5 x IQR
Upper Inner Fence (UIF) = 8 + 1.5 x 4
Upper Inner Fence (UIF) = 8 + 6
Upper Inner Fence (UIF) = 14

Calculate Lower Outer Fence (LOF):

Lower Outer Fence (LOF) = LQ - 3 x IQR
Lower Outer Fence (LOF) = 4 - 3 x 4
Lower Outer Fence (LOF) = 4 - 12
Lower Outer Fence (LOF) = -8

Calculate Upper Outer Fence (UOF):

Upper Outer Fence (UOF) = UQ + 3 x IQR
Upper Outer Fence (UOF) = 8 + 3 x 4
Upper Outer Fence (UOF) = 8 + 12
Upper Outer Fence (UOF) = 20

Calculate Suspect Outliers:

Suspect Outliers are values between the inner and outer fences
We wish to mark all values in our dataset (v) in red below such that
-8 < v < -2 and 14 < v < 20
2,4,6,8,10

Calculate Highly Suspect Outliers:

Highly Suspect Outliers are values outside the outer fences
Mark all values in our dataset (v) in red below such that
v < -8 or v > 20
2,4,6,8,10

Stem and Leaf Plot

Take the first digit of each value in our number set
Use this as our stem value
Use the remaining digits for our leaf portion

Sort our number set in descending order:

{10,8,6,4,2}

Stem and Leaf Plot

Stem	Leaf
1	0
8
6
4
2

Ranked Data Calculation

Sort our number set in ascending order
and assign a ranking to each number:

Ranked Data Table

Number Set Value	2	4	6	8	10
Rank	1	2	3	4	5

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

Assign ranks from lowest to highest (1 to 5)
Our original number set in unsorted order was 2,4,6,8,10
Our respective ranked data set is 1,2,3,4,5

Root Mean Square Calculation

Root Mean Square =	√A
	√N

where A = x₁² + x₂² + x₃² + x₄² + x₅² and N = 5 number set items

Calculate A

A = 2² + 4² + 6² + 8² + 10²
A = 4 + 16 + 36 + 64 + 100
A = 220

Calculate Root Mean Square (RMS):

RMS =	√220
	√5

RMS =	14.832396974191
	2.2360679774998

RMS = 6.6332495807108

Harmonic-Geometric-Mid Range Weighted Average

Calculate the harmonic mean,
geometric mean, mid-range, weighted-average:

Calculate Harmonic Mean:

Harmonic Mean =	N
	1/x₁ + 1/x₂ + 1/x₃ + 1/x₄ + 1/x₅

With N = 5 and each x_i a member of the number set you entered, we have:

Harmonic Mean =	5
	1/2 + 1/4 + 1/6 + 1/8 + 1/10

Harmonic Mean =	5
	0.5 + 0.25 + 0.16666666666667 + 0.125 + 0.1

Harmonic Mean =	5
	1.1416666666667

Harmonic Mean = 4.3795620437956

Calculate Geometric Mean:

Geometric Mean = (x₁ * x₂ * x₃ * x₄ * x₅)^1/N
Geometric Mean = (2 * 4 * 6 * 8 * 10)^1/5
Geometric Mean = 3840^0.2
Geometric Mean = 5.2103421693947

Calcualte Mid-Range:

Mid-Range =	Maximum Value in Number Set + Minimum Value in Number Set
	2

Mid-Range =	10 + 2
	2

Mid-Range =	12
	2

Mid-Range = 6

Calculate weighted average

2,4,6,8,10

Weighted-Average Formula:

Multiply each value by each probability amount
We do this by multiplying each X_i x p_i to get a weighted score Y

Weighted Average =	X₁p₁ + X₂p₂ + X₃p₃ + X₄p₄ + X₅p₅
	n

Weighted Average =	2 x 0.2 + 4 x 0.4 + 6 x 0.6 + 8 x 0.8 + 10 x 0.9
	5

Weighted Average =	0.4 + 1.6 + 3.6 + 6.4 + 9
	5

Weighted Average =	21
	5

Weighted Average = 4.2

Frequency Distribution Table

Show the freqency distribution table for this number set
2, 4, 6, 8, 10

Determine the Number of Intervals using Sturges Rule:

We need to choose the smallest integer k such that 2^k ≥ n where n = 5
For k = 1, we have 2¹ = 2
For k = 2, we have 2² = 4
For k = 3, we have 2³ = 8 ← Use this since it is greater than our n value of 5
Therefore, we use 3 intervals
Our maximum value in our number set of 10 - 2 = 8
Each interval size is the difference of the maximum and minimum value divided by the number of intervals

Interval Size =	8
	3

Add 1 to this giving us 2 + 1 = 3

Frequency Distribution Table

Class Limits	Class Boundaries	FD	CFD	RFD	CRFD
2 - 5	1.5 - 5.5	2	2	2/5 = 40%	2/5 = 40%
5 - 8	4.5 - 8.5	1	2 + 1 = 3	1/5 = 20%	3/5 = 60%
8 - 11	7.5 - 11.5	2	2 + 1 + 2 = 5	2/5 = 40%	5/5 = 100%
		5		100%

Successive Ratio Calculation

Go through our 5 numbers
Determine the ratio of each number to the next one

Successive Ratio 1: 2,4,6,8,10

2:4 → 0.5

Successive Ratio 2: 2,4,6,8,10

4:6 → 0.6667

Successive Ratio 3: 2,4,6,8,10

6:8 → 0.75

Successive Ratio 4: 2,4,6,8,10

8:10 → 0.8

Successive Ratio Answer

Successive Ratio = 2:4,4:6,6:8,8:10 or 0.5,0.6667,0.75,0.8

Treat this as a set

Calculate the power set and partitions
For set S = {2,4,6,8,10}, show:
Elements, cardinality, and power set

List the elements of S

Elements = set objects
Use the ∈ symbol.

2 ∈ S
4 ∈ S
6 ∈ S
8 ∈ S
10 ∈ S

Cardinality of set S → |S|:

Cardinality = Number of set elements.
Since the set S contains 5 elements
|S| = 5

Determine the power set P:

Power set = Set of all subsets of S
including S and ∅.

Calculate power set subsets

S contains 5 terms
Power Set contains 2⁵ = 32 items

Build subsets of P

The subset A of a set B is
A set where all elements of A are in B.

#	Binary	Use if 1	Subset
0	00000	2,4,6,8,10	{}
1	00001	2,4,6,8,10	{10}
2	00010	2,4,6,8,10	{8}
3	00011	2,4,6,8,10	{8,10}
4	00100	2,4,6,8,10	{6}
5	00101	2,4,6,8,10	{6,10}
6	00110	2,4,6,8,10	{6,8}
7	00111	2,4,6,8,10	{6,8,10}
8	01000	2,4,6,8,10	{4}
9	01001	2,4,6,8,10	{4,10}
10	01010	2,4,6,8,10	{4,8}
11	01011	2,4,6,8,10	{4,8,10}
12	01100	2,4,6,8,10	{4,6}
13	01101	2,4,6,8,10	{4,6,10}
14	01110	2,4,6,8,10	{4,6,8}
15	01111	2,4,6,8,10	{4,6,8,10}
16	10000	2,4,6,8,10	{2}
17	10001	2,4,6,8,10	{2,10}
18	10010	2,4,6,8,10	{2,8}
19	10011	2,4,6,8,10	{2,8,10}
20	10100	2,4,6,8,10	{2,6}
21	10101	2,4,6,8,10	{2,6,10}
22	10110	2,4,6,8,10	{2,6,8}
23	10111	2,4,6,8,10	{2,6,8,10}
24	11000	2,4,6,8,10	{2,4}
25	11001	2,4,6,8,10	{2,4,10}
26	11010	2,4,6,8,10	{2,4,8}
27	11011	2,4,6,8,10	{2,4,8,10}
28	11100	2,4,6,8,10	{2,4,6}
29	11101	2,4,6,8,10	{2,4,6,10}
30	11110	2,4,6,8,10	{2,4,6,8}
31	11111	2,4,6,8,10	{2,4,6,8,10}

List our Power Set P in notation form:

P = {{}, {2}, {4}, {6}, {8}, {10}, {2,10}, {2,4}, {2,6}, {2,8}, {4,10}, {4,6}, {4,8}, {6,10}, {6,8}, {8,10}, {2,4,10}, {2,4,6}, {2,4,8}, {2,6,10}, {2,6,8}, {2,8,10}, {4,6,10}, {4,6,8}, {4,8,10}, {6,8,10}, {2,4,6,10}, {2,4,6,8}, {2,4,8,10}, {2,6,8,10}, {4,6,8,10}, {2,4,6,8,10}}

Partition 1

{8,10},{2,4,6}

Partition 2

{8,10},{2,4,6}

Partition 3

{8,10},{2,4,6}

Partition 4

{6,10},

Partition 5

{6,10},

Partition 6

{6,10},

Partition 7

{6,8},

Partition 8

{6,8},

Partition 9

{6,8},

Partition 10

{6,8,10},{2,4}

Partition 11

{6,8,10},{2,4}

Partition 12

{4,10},{2,4,6}

Partition 13

{4,10},{2,4,6}

Partition 14

{4,10},{2,4,6}

Partition 15

{4,8},{2,4,6}

Partition 16

{4,8},{2,4,6}

Partition 17

{4,8},{2,4,6}

Partition 18

{4,8,10},

Partition 19

{4,8,10},

Partition 20

{4,6},

Partition 21

{4,6},

Partition 22

{4,6},

Partition 23

{4,6,10},

Partition 24

{4,6,10},

Partition 25

{4,6,8},

Partition 26

{4,6,8},

Partition 27

{4,6,8,10},{2}

Partition 28

{2,10},{2,4,6}

Partition 29

{2,10},{2,4,6}

Partition 30

{2,10},{2,4,6}

Partition 31

{2,8},{2,4,6}

Partition 32

{2,8},{2,4,6}

Partition 33

{2,8},{2,4,6}

Partition 34

{2,8,10},{2,4}

Partition 35

{2,8,10},{2,4}

Partition 36

{2,6},

Partition 37

{2,6},

Partition 38

{2,6},

Partition 39

{2,6,10},{2,4}

Partition 40

{2,6,10},{2,4}

Partition 41

{2,6,8},{2,4}

Partition 42

{2,6,8},{2,4}

Partition 43

{2,6,8,10},

Partition 44

{2,4},{2,4,6}

Partition 45

{2,4},{2,4,6}

Partition 46

{2,4},{2,4,6}

Partition 47

{2,4,10},

Partition 48

{2,4,10},

Partition 49

{2,4,8},

Partition 50

{2,4,8},

Partition 51

{2,4,8,10},

Partition 52

{2,4,6},

Partition 53

{2,4,6},

Partition 54

{2,4,6,10},

Partition 55

{2,4,6,8},

Partition 56

{{2},{4},{6},{8},{10})

Treat this as a Vector

(a₁, a₂, a₃, a₄, a₅) = (2, 4, 6, 8, 10)

Calculate the magnitude:

||A|| = Square Root(a₁² + a₂² + a₃² + a₄² + a₅²)
||A|| = Square Root(2² + 4² + 6² + 8² + 10²)
||A|| = √4 + 16 + 36 + 64 + 100
||A|| = √220
||A|| = 14.832396974191

Treat this as a sequence

Find the explicit formula and terms
Calculate the explicit formula
Calculate term number 10
And the Sum of the first 10 terms for:
2,4,6,8,10

Explicit Formula

a_n = a₁ + (n - 1)d

Define d

d = Δ between consecutive terms
d = a_n - a_{n - 1}

We see a common difference = 2
We have a₁ = 2
a_n = 2 + 2(n - 1)

Calculate Term (6)

Plug in n = 6 and d = 2
a₆ = 2 + 2(6 - 1)
a₆ = 2 + 2(6 - 1)
a₆ = 2 + 2(5)
a₆ = 2 + 10
a₆ = 12

Calculate Term (7)

Plug in n = 7 and d = 2
a₇ = 2 + 2(7 - 1)
a₇ = 2 + 2(7 - 1)
a₇ = 2 + 2(6)
a₇ = 2 + 12
a₇ = 14

Calculate Term (8)

Plug in n = 8 and d = 2
a₈ = 2 + 2(8 - 1)
a₈ = 2 + 2(8 - 1)
a₈ = 2 + 2(7)
a₈ = 2 + 14
a₈ = 16

Calculate Term (9)

Plug in n = 9 and d = 2
a₉ = 2 + 2(9 - 1)
a₉ = 2 + 2(9 - 1)
a₉ = 2 + 2(8)
a₉ = 2 + 16
a₉ = 18

Calculate Term (10)

Plug in n = 10 and d = 2
a₁₀ = 2 + 2(10 - 1)
a₁₀ = 2 + 2(10 - 1)
a₁₀ = 2 + 2(9)
a₁₀ = 2 + 18
a₁₀ = 20

Calculate S_n:

S_n = Sum of the first n terms

S_n =	n(a₁ + a_n)
	2

Substituting n = 10, we get:

S₁₀ =	10(a₁ + a₁₀)
	2

S₁₀ =	10(2 + 20)
	2

S₁₀ =	10(22)
	2

S₁₀ =	220
	2

S₁₀ = 110

Final Answers

What is the Answer?

Order lowest to highest = 2 < 4 < 6 < 8 < 10
Order highest to lowest = 10 > 8 > 6 > 4 > 2
μ = 6
σ² = 44
σ = 6.6332
SEM = 3.3166
Skewness = 1.5418539495248
Average Deviation = 6
Median = 6
Mode = N/A
Range = 8
Mid-Range = 6
PSC1 = No Pearsons Skewness Coefficient
PSC2 = -2.7136
Entropy = 1.6094379124341
1,2,3,4,5
RMS = 6.6332495807108
Harmonic Mean = 4.3795620437956Geometric Mean = 5.2103421693947
Mid-Range = 6
Weighted Average = 4.2
Successive Ratio = Successive Ratio = 2:4,4:6,6:8,8:10 or 0.5,0.6667,0.75,0.8
P = {{}, {2}, {4}, {6}, {8}, {10}, {2,10}, {2,4}, {2,6}, {2,8}, {4,10}, {4,6}, {4,8}, {6,10}, {6,8}, {8,10}, {2,4,10}, {2,4,6}, {2,4,8}, {2,6,10}, {2,6,8}, {2,8,10}, {4,6,10}, {4,6,8}, {4,8,10}, {6,8,10}, {2,4,6,10}, {2,4,6,8}, {2,4,8,10}, {2,6,8,10}, {4,6,8,10}, {2,4,6,8,10}}
||A|| = 14.832396974191
S₁₀ = 110

How does the Basic Statistics Calculator work?

Free Basic Statistics Calculator - Given a number set, and an optional probability set, this calculates the following statistical items:
Expected Value
Mean = μ
Variance = σ²
Standard Deviation = σ
Standard Error of the Mean
Skewness
Mid-Range
Average Deviation (Mean Absolute Deviation)
Median
Mode
Range
Pearsons Skewness Coefficients
Entropy
Upper Quartile (hinge) (75th Percentile)
Lower Quartile (hinge) (25th Percentile)
InnerQuartile Range
Inner Fences (Lower Inner Fence and Upper Inner Fence)
Outer Fences (Lower Outer Fence and Upper Outer Fence)
Suspect Outliers
Highly Suspect Outliers
Stem and Leaf Plot
Ranked Data Set
Central Tendency Items such as Harmonic Mean and Geometric Mean and Mid-Range
Root Mean Square
Weighted Average (Weighted Mean)
Frequency Distribution
Successive Ratio
This calculator has 2 inputs.

What 8 formulas are used for the Basic Statistics Calculator?

Root Mean Square = √A/√N
Successive Ratio = n₁/n₀
μ = ΣX_i/n
Mode = Highest Frequency Number
Mid-Range = (Maximum Value in Number Set + Minimum Value in Number Set)/2
Quartile: V = y(n + 1)/100
σ² = ΣE(X_i - μ)²/n

For more math formulas, check out our Formula Dossier

What 20 concepts are covered in the Basic Statistics Calculator?

average deviation: Mean of the absolute values of the distance from the mean for each number in a number set
basic statistics
central tendency: a central or typical value for a probability distribution. Typical measures are the mode, median, mean
entropy: refers to disorder or uncertainty
expected value: predicted value of a variable or event
E(X) = Σx_I · P(x)
frequency distribution: frequency measurement of various outcomes
inner fence: ut-off values for upper and lower outliers in a dataset
mean: A statistical measurement also known as the average
median: the value separating the higher half from the lower half of a data sample,
mode: the number that occurs the most in a number set
outer fence: start with the IQR and multiply this number by 3. We then subtract this number from the first quartile and add it to the third quartile. These two numbers are our outer fences.
outlier: an observation that lies an abnormal distance from other values in a random sample from a population
quartile: 1 of 4 equal groups in the distribution of a number set
range: Difference between the largest and smallest values in a number set
rank: the data transformation in which numerical or ordinal values are replaced by their rank when the data are sorted.
sample space: the set of all possible outcomes or results of that experiment.
standard deviation: a measure of the amount of variation or dispersion of a set of values. The square root of variance
stem and leaf plot: a technique used to classify either discrete or continuous variables. A stem and leaf plot is used to organize data as they are collected. A stem and leaf plot looks something like a bar graph. Each number in the data is broken down into a stem and a leaf, thus the name.
variance: How far a set of random numbers are spead out from the mean
weighted average: An average of numbers using probabilities for each event as a weighting

Example calculations for the Basic Statistics Calculator

Tags:

Add This Calculator To Your Website

Calculate Root Mean Square from 2,4,6,8,10

Order This Number Set

Basic Stats Calculations

Calculate Mean (Average) denoted as μ

Calculate variance denoted as σ2

Add our 5 sum of squared differences up

Variance Table

Calculate the Standard Error of the Mean:

Calculate Skewness:

Adding our 5 sum of cubed differences

Finish calculating skewness:

Calculate Average Deviation (Mean Absolute Deviation) denoted below:

Add our 5 absolute value of differences from the mean

Calculate average deviation (mean absolute deviation)

Calculate the Median (Middle Value)

Final Median Calculation

Calculate the Mode - Highest Frequency Number

Calculate the Range

Calculate Mid-Range:

Calculate Pearsons Skewness Coefficient 1:

Calculate Pearsons Skewness Coefficient 2:

Calculate Entropy:

Calculate the Quartile Items

Calculate Upper Quartile (UQ) when y = 75%:

Calculate Lower Quartile (LQ) when y = 25%:

Calculate Inter-Quartile Range (IQR):

Calculate Lower Inner Fence (LIF):

Calculate Upper Inner Fence (UIF):

Calculate Lower Outer Fence (LOF):

Calculate Upper Outer Fence (UOF):

Calculate Suspect Outliers:

Calculate Highly Suspect Outliers:

Stem and Leaf Plot

Sort our number set in descending order:

Stem and Leaf Plot

Ranked Data Calculation

Ranked Data Table

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

Root Mean Square Calculation

Calculate A

Calculate Root Mean Square (RMS):

Harmonic-Geometric-Mid Range Weighted Average

Calculate Harmonic Mean:

Calculate Geometric Mean:

Calcualte Mid-Range:

Calculate weighted average

Weighted-Average Formula:

Frequency Distribution Table

Determine the Number of Intervals using Sturges Rule:

Frequency Distribution Table

Successive Ratio Calculation

Successive Ratio 1: 2,4,6,8,10

Successive Ratio 2: 2,4,6,8,10

Successive Ratio 3: 2,4,6,8,10

Successive Ratio 4: 2,4,6,8,10

Successive Ratio Answer

Treat this as a set

List the elements of S

Cardinality of set S → |S|:

Determine the power set P:

Calculate power set subsets

Build subsets of P

List our Power Set P in notation form:

Partition 1

Partition 2

Partition 3

Partition 4

Partition 5

Partition 6

Partition 7

Partition 8

Partition 9

Partition 10

Partition 11

Partition 12

Partition 13

Partition 14

Partition 15

Partition 16

Partition 17

Calculate variance denoted as σ²

Calculate S_n: