Calculate Number Set Basics from 9,8,7,64,3,2,1

<-- Enter Number Set
<-- Probabilities (or counts for Weighted Average), check box if you are using these →
  

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You entered a number set X of {9,8,7,64,3,2,1}
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
1 < 2 < 3 < 7 < 8 < 9 < 64

Order highest to lowest
64 > 9 > 8 > 7 > 3 > 2 > 1

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  =	ΣXi
	n

μ  =	9 + 8 + 7 + 64 + 3 + 2 + 1
	7

μ  =	94
	7

μ = 13.428571428571

Calculate variance denoted as σ²

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

(X₁ - μ)² = (9 - μ = 13.428571428571)² = 9² = 81
(X₂ - μ)² = (8 - μ = 13.428571428571)² = 8² = 64
(X₃ - μ)² = (7 - μ = 13.428571428571)² = 7² = 49
(X₄ - μ)² = (64 - μ = 13.428571428571)² = 64² = 4096
(X₅ - μ)² = (3 - μ = 13.428571428571)² = 3² = 9
(X₆ - μ)² = (2 - μ = 13.428571428571)² = 2² = 4
(X₇ - μ)² = (1 - μ = 13.428571428571)² = 1² = 1

Add our 7 sum of squared differences up

ΣE(X_i - μ)² = 81 + 64 + 49 + 4096 + 9 + 4 + 1
ΣE(X_i - μ)² = 4304

Variance Table

Population	Sample
σ2  =   ΣE(Xi - μ)2    n	σ2  =   ΣE(Xi - μ)2    n - 1
σ2  =   4304    7	σ2  =   4304    6
Variance: σp2 = 614.85714285714	Variance: σs2 = 717.33333333333
Standard Deviation: σp = √σp2 = √614.85714285714	Standard Deviation: σs = √σs2 = √717.33333333333
Standard Deviation: σp = 24.7963	Standard Deviation: σs = 26.7831

Calculate the Standard Error of the Mean:

Population	Sample
SEM  =   σp    √n	SEM  =   σs    √n
SEM  =   24.7963    √7	SEM  =   26.7831    √7
SEM  =   24.7963    2.6457513110646	SEM  =   26.7831    2.6457513110646
SEM = 9.3721	SEM = 10.1231

Calculate Skewness:

Skewness  =	E(Xi - μ)3
	(n - 1)σ3

Let's evaluate the square difference from the mean of each term (X_i - μ)³:
(X₁ - μ)³ = (9 - μ = 13.428571428571)³ = 9³ = 729
(X₂ - μ)³ = (8 - μ = 13.428571428571)³ = 8³ = 512
(X₃ - μ)³ = (7 - μ = 13.428571428571)³ = 7³ = 343
(X₄ - μ)³ = (64 - μ = 13.428571428571)³ = 64³ = 262144
(X₅ - μ)³ = (3 - μ = 13.428571428571)³ = 3³ = 27
(X₆ - μ)³ = (2 - μ = 13.428571428571)³ = 2³ = 8
(X₇ - μ)³ = (1 - μ = 13.428571428571)³ = 1³ = 1

Adding our 7 sum of cubed differences

ΣE(X_i - μ)³ = 729 + 512 + 343 + 262144 + 27 + 8 + 1
ΣE(X_i - μ)³ = 263764

Finish calculating skewness:

Skewness  =	E(Xi - μ)3
	(n - 1)σ3

Skewness  =	263764
	(7 - 1)24.79633

Skewness  =	263764
	(6)15246.166074485

Skewness  =	263764
	91476.996446912

Skewness = 2.8833915655842

Calculate Average Deviation (Mean Absolute Deviation) denoted below:

AD  =	Σ|Xi - μ|
	n

Let's evaluate the absolute value of the difference from the mean of each term |X_i - μ|:
|X₁ - μ| = |9 - μ = 13.428571428571| = |9| = 9
|X₂ - μ| = |8 - μ = 13.428571428571| = |8| = 8
|X₃ - μ| = |7 - μ = 13.428571428571| = |7| = 7
|X₄ - μ| = |64 - μ = 13.428571428571| = |64| = 64
|X₅ - μ| = |3 - μ = 13.428571428571| = |3| = 3
|X₆ - μ| = |2 - μ = 13.428571428571| = |2| = 2
|X₇ - μ| = |1 - μ = 13.428571428571| = |1| = 1

Add our 7 absolute value of differences from the mean

Σ|X_i - μ| = 9 + 8 + 7 + 64 + 3 + 2 + 1
Σ|X_i - μ| = 94

Calculate average deviation (mean absolute deviation)

AD  =	Σ|Xi - μ|
	n

AD  =	94
	7

Average Deviation = 13.42857

Calculate the Median (Middle Value)

Since our number set contains 7 elements which is an odd number
our median number is determined as follows:
Number Set = (n₁,n₂,n₃,n₄,n₅,n₆,n₇)
Median Number = Entry ½(n + 1)
Median Number = Entry ½(8)
Median Number = n₄

Final Median Calculation

Therefore, we sort our number set in ascending order and our median is
entry 4 of our number set highlighted in red:
(
1)
,2)
,3)
,7)
,8)
,9)
,64)
Median = 7

Calculate the Mode - Highest Frequency Number

The highest frequency of occurence in our number set is
1 times by the following numbers in green:
(9,8,7,64,3,2,1)
Since the maximum frequency of any number is 1, no mode exists.

Calculate the Range

Range = Largest Number - Smallest Number
Range = 64 - 1
Range = 63

Calculate Mid-Range:

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

Mid-Range  =	64 + 1
	2

Mid-Range  =	65
	2

Mid-Range = 32.5

Calculate Pearsons Skewness Coefficient 1:

PSC1  =	μ - Mode
	σ

PSC1  =	3( μ = 13.428571428571 - N/A)
	24.7963

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 = 13.428571428571 - 7)
	24.7963

PSC2  =	3 x -7
	24.7963

PSC2  =	-21
	24.7963

PSC2 = -0.8469

Calculate Entropy:

Entropy = Ln(n)
Entropy = Ln(7)
Entropy = 1.9459101490553

Calculate the Quartile Items

Sort our number set from lowest to highest
{1,2,3,7,8,9,64}

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

V  =	y(n + 1)
	100

V  =	75(7 + 1)
	100

V  =	75(8)
	100

V  =	600
	100

V = 6 ← Rounded down to the nearest integer

Upper quartile (UQ) point = Point # 6 in the dataset which is 9
1,2,3,7,8,9,64

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

V  =	y(n + 1)
	100

V  =	25(7 + 1)
	100

V  =	25(8)
	100

V  =	200
	100

V = 2 ← Rounded up to the nearest integer

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

1,2,3,7,8,9,64

Calculate Inter-Quartile Range (IQR):

IQR = UQ - LQ
IQR = 9 - 2
IQR = 7

Calculate Lower Inner Fence (LIF):

Lower Inner Fence (LIF) = LQ - 1.5 x IQR
Lower Inner Fence (LIF) = 2 - 1.5 x 7
Lower Inner Fence (LIF) = 2 - 10.5
Lower Inner Fence (LIF) = -8.5

Calculate Upper Inner Fence (UIF):

Upper Inner Fence (UIF) = UQ + 1.5 x IQR
Upper Inner Fence (UIF) = 9 + 1.5 x 7
Upper Inner Fence (UIF) = 9 + 10.5
Upper Inner Fence (UIF) = 19.5

Calculate Lower Outer Fence (LOF):

Lower Outer Fence (LOF) = LQ - 3 x IQR
Lower Outer Fence (LOF) = 2 - 3 x 7
Lower Outer Fence (LOF) = 2 - 21
Lower Outer Fence (LOF) = -19

Calculate Upper Outer Fence (UOF):

Upper Outer Fence (UOF) = UQ + 3 x IQR
Upper Outer Fence (UOF) = 9 + 3 x 7
Upper Outer Fence (UOF) = 9 + 21
Upper Outer Fence (UOF) = 30

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
-19 < v < -8.5 and 19.5 < v < 30
1,2,3,7,8,9,64

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 < -19 or v > 30
1,2,3,7,8,9,64

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:

{64,9,8,7,3,2,1}

Stem and Leaf Plot

Stem	Leaf
6	4
9
8
7
3
2
1

Ranked Data Calculation

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

Ranked Data Table

Number Set Value	1	2	3	7	8	9	64
Rank	1	2	3	4	5	6	7

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

Assign ranks from lowest to highest (1 to 7)
Our original number set in unsorted order was 1,2,3,7,8,9,64
Our respective ranked data set is 1,2,3,4,5,6,7

Root Mean Square Calculation

Root Mean Square  =	√A
	√N

where A = x₁² + x₂² + x₃² + x₄² + x₅² + x₆² + x₇² and N = 7 number set items

Calculate A

A = 1² + 2² + 3² + 7² + 8² + 9² + 64²
A = 1 + 4 + 9 + 49 + 64 + 81 + 4096
A = 4304

Calculate Root Mean Square (RMS):

RMS  =	√4304
	√7

RMS  =	65.604877867427
	2.6457513110646

RMS = 24.796313089997

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 + 1/x6 + 1/x7

With N = 7 and each x_i a member of the number set you entered, we have:

Harmonic Mean  =	7
	1/1 + 1/2 + 1/3 + 1/7 + 1/8 + 1/9 + 1/64

Harmonic Mean  =	7
	1 + 0.5 + 0.33333333333333 + 0.14285714285714 + 0.125 + 0.11111111111111 + 0.015625

Harmonic Mean  =	7
	2.2279265873016

Harmonic Mean = 3.1419347656685

Calculate Geometric Mean:

Geometric Mean = (x₁ * x₂ * x₃ * x₄ * x₅ * x₆ * x₇)^1/N
Geometric Mean = (1 * 2 * 3 * 7 * 8 * 9 * 64)^1/7
Geometric Mean = 193536^{0.14285714285714}
Geometric Mean = 5.691826851234

Calcualte Mid-Range:

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

Mid-Range  =	64 + 1
	2

Mid-Range  =	65
	2

Mid-Range = 32.5

Calculate weighted average

9,8,7,64,3,2,1

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 + X6p6 + X7p7
	n

Weighted Average  =	9 x 0.2 + 8 x 0.4 + 7 x 0.6 + 64 x 0.8 + 3 x 0.9 + 2 x + 1 x
	7

Weighted Average  =	1.8 + 3.2 + 4.2 + 51.2 + 2.7 + 0 + 0
	7

Weighted Average  =	63.1
	7

Weighted Average = 9.0142857142857

Frequency Distribution Table

Show the freqency distribution table for this number set
1, 2, 3, 7, 8, 9, 64

Determine the Number of Intervals using Sturges Rule:

We need to choose the smallest integer k such that 2^k ≥ n where n = 7
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 7
Therefore, we use 3 intervals
Our maximum value in our number set of 64 - 1 = 63
Each interval size is the difference of the maximum and minimum value divided by the number of intervals

Interval Size  =	63
	3

Add 1 to this giving us 21 + 1 = 22

Frequency Distribution Table

Class Limits	Class Boundaries	FD	CFD	RFD	CRFD
1 - 23	0.5 - 23.5	6	6	6/7 = 85.71%	6/7 = 85.71%
23 - 45	22.5 - 45.5		6 + = 6	/7 = 0%	6/7 = 85.71%
45 - 67	44.5 - 67.5	1	6 + + 1 = 7	1/7 = 14.29%	7/7 = 100%
		7		100%

Successive Ratio Calculation

Go through our 7 numbers
Determine the ratio of each number to the next one

Successive Ratio 1: 1,2,3,7,8,9,64

1:2 → 0.5

Successive Ratio 2: 1,2,3,7,8,9,64

2:3 → 0.6667

Successive Ratio 3: 1,2,3,7,8,9,64

3:7 → 0.4286

Successive Ratio 4: 1,2,3,7,8,9,64

7:8 → 0.875

Successive Ratio 5: 1,2,3,7,8,9,64

8:9 → 0.8889

Successive Ratio 6: 1,2,3,7,8,9,64

9:64 → 0.1406

Successive Ratio Answer

Successive Ratio = 1:2,2:3,3:7,7:8,8:9,9:64 or 0.5,0.6667,0.4286,0.875,0.8889,0.1406

Treat this as a set

Calculate the power set and partitions
For set S = {9,8,7,64,3,2,1}, show:
Elements, cardinality, and power set

List the elements of S

Elements = set objects
Use the ∈ symbol.

1. 9 ∈ S
2. 8 ∈ S
3. 7 ∈ S
4. 64 ∈ S
5. 3 ∈ S
6. 2 ∈ S
7. 1 ∈ S

Cardinality of set S → |S|:

Cardinality = Number of set elements.
Since the set S contains 7 elements
|S| = 7

Determine the power set P:

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

Calculate power set subsets

S contains 7 terms
Power Set contains 2⁷ = 128 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	0000000	9,8,7,64,3,2,1	{}
1	0000001	9,8,7,64,3,2,1	{1}
2	0000010	9,8,7,64,3,2,1	{2}
3	0000011	9,8,7,64,3,2,1	{2,1}
4	0000100	9,8,7,64,3,2,1	{3}
5	0000101	9,8,7,64,3,2,1	{3,1}
6	0000110	9,8,7,64,3,2,1	{3,2}
7	0000111	9,8,7,64,3,2,1	{3,2,1}
8	0001000	9,8,7,64,3,2,1	{64}
9	0001001	9,8,7,64,3,2,1	{64,1}
10	0001010	9,8,7,64,3,2,1	{64,2}
11	0001011	9,8,7,64,3,2,1	{64,2,1}
12	0001100	9,8,7,64,3,2,1	{64,3}
13	0001101	9,8,7,64,3,2,1	{64,3,1}
14	0001110	9,8,7,64,3,2,1	{64,3,2}
15	0001111	9,8,7,64,3,2,1	{64,3,2,1}
16	0010000	9,8,7,64,3,2,1	{7}
17	0010001	9,8,7,64,3,2,1	{7,1}
18	0010010	9,8,7,64,3,2,1	{7,2}
19	0010011	9,8,7,64,3,2,1	{7,2,1}
20	0010100	9,8,7,64,3,2,1	{7,3}
21	0010101	9,8,7,64,3,2,1	{7,3,1}
22	0010110	9,8,7,64,3,2,1	{7,3,2}
23	0010111	9,8,7,64,3,2,1	{7,3,2,1}
24	0011000	9,8,7,64,3,2,1	{7,64}
25	0011001	9,8,7,64,3,2,1	{7,64,1}
26	0011010	9,8,7,64,3,2,1	{7,64,2}
27	0011011	9,8,7,64,3,2,1	{7,64,2,1}
28	0011100	9,8,7,64,3,2,1	{7,64,3}
29	0011101	9,8,7,64,3,2,1	{7,64,3,1}
30	0011110	9,8,7,64,3,2,1	{7,64,3,2}
31	0011111	9,8,7,64,3,2,1	{7,64,3,2,1}
32	0100000	9,8,7,64,3,2,1	{8}
33	0100001	9,8,7,64,3,2,1	{8,1}
34	0100010	9,8,7,64,3,2,1	{8,2}
35	0100011	9,8,7,64,3,2,1	{8,2,1}
36	0100100	9,8,7,64,3,2,1	{8,3}
37	0100101	9,8,7,64,3,2,1	{8,3,1}
38	0100110	9,8,7,64,3,2,1	{8,3,2}
39	0100111	9,8,7,64,3,2,1	{8,3,2,1}
40	0101000	9,8,7,64,3,2,1	{8,64}
41	0101001	9,8,7,64,3,2,1	{8,64,1}
42	0101010	9,8,7,64,3,2,1	{8,64,2}
43	0101011	9,8,7,64,3,2,1	{8,64,2,1}
44	0101100	9,8,7,64,3,2,1	{8,64,3}
45	0101101	9,8,7,64,3,2,1	{8,64,3,1}
46	0101110	9,8,7,64,3,2,1	{8,64,3,2}
47	0101111	9,8,7,64,3,2,1	{8,64,3,2,1}
48	0110000	9,8,7,64,3,2,1	{8,7}
49	0110001	9,8,7,64,3,2,1	{8,7,1}
50	0110010	9,8,7,64,3,2,1	{8,7,2}
51	0110011	9,8,7,64,3,2,1	{8,7,2,1}
52	0110100	9,8,7,64,3,2,1	{8,7,3}
53	0110101	9,8,7,64,3,2,1	{8,7,3,1}
54	0110110	9,8,7,64,3,2,1	{8,7,3,2}
55	0110111	9,8,7,64,3,2,1	{8,7,3,2,1}
56	0111000	9,8,7,64,3,2,1	{8,7,64}
57	0111001	9,8,7,64,3,2,1	{8,7,64,1}
58	0111010	9,8,7,64,3,2,1	{8,7,64,2}
59	0111011	9,8,7,64,3,2,1	{8,7,64,2,1}
60	0111100	9,8,7,64,3,2,1	{8,7,64,3}
61	0111101	9,8,7,64,3,2,1	{8,7,64,3,1}
62	0111110	9,8,7,64,3,2,1	{8,7,64,3,2}
63	0111111	9,8,7,64,3,2,1	{8,7,64,3,2,1}
64	1000000	9,8,7,64,3,2,1	{9}
65	1000001	9,8,7,64,3,2,1	{9,1}
66	1000010	9,8,7,64,3,2,1	{9,2}
67	1000011	9,8,7,64,3,2,1	{9,2,1}
68	1000100	9,8,7,64,3,2,1	{9,3}
69	1000101	9,8,7,64,3,2,1	{9,3,1}
70	1000110	9,8,7,64,3,2,1	{9,3,2}
71	1000111	9,8,7,64,3,2,1	{9,3,2,1}
72	1001000	9,8,7,64,3,2,1	{9,64}
73	1001001	9,8,7,64,3,2,1	{9,64,1}
74	1001010	9,8,7,64,3,2,1	{9,64,2}
75	1001011	9,8,7,64,3,2,1	{9,64,2,1}
76	1001100	9,8,7,64,3,2,1	{9,64,3}
77	1001101	9,8,7,64,3,2,1	{9,64,3,1}
78	1001110	9,8,7,64,3,2,1	{9,64,3,2}
79	1001111	9,8,7,64,3,2,1	{9,64,3,2,1}
80	1010000	9,8,7,64,3,2,1	{9,7}
81	1010001	9,8,7,64,3,2,1	{9,7,1}
82	1010010	9,8,7,64,3,2,1	{9,7,2}
83	1010011	9,8,7,64,3,2,1	{9,7,2,1}
84	1010100	9,8,7,64,3,2,1	{9,7,3}
85	1010101	9,8,7,64,3,2,1	{9,7,3,1}
86	1010110	9,8,7,64,3,2,1	{9,7,3,2}
87	1010111	9,8,7,64,3,2,1	{9,7,3,2,1}
88	1011000	9,8,7,64,3,2,1	{9,7,64}
89	1011001	9,8,7,64,3,2,1	{9,7,64,1}
90	1011010	9,8,7,64,3,2,1	{9,7,64,2}
91	1011011	9,8,7,64,3,2,1	{9,7,64,2,1}
92	1011100	9,8,7,64,3,2,1	{9,7,64,3}
93	1011101	9,8,7,64,3,2,1	{9,7,64,3,1}
94	1011110	9,8,7,64,3,2,1	{9,7,64,3,2}
95	1011111	9,8,7,64,3,2,1	{9,7,64,3,2,1}
96	1100000	9,8,7,64,3,2,1	{9,8}
97	1100001	9,8,7,64,3,2,1	{9,8,1}
98	1100010	9,8,7,64,3,2,1	{9,8,2}
99	1100011	9,8,7,64,3,2,1	{9,8,2,1}
100	1100100	9,8,7,64,3,2,1	{9,8,3}
101	1100101	9,8,7,64,3,2,1	{9,8,3,1}
102	1100110	9,8,7,64,3,2,1	{9,8,3,2}
103	1100111	9,8,7,64,3,2,1	{9,8,3,2,1}
104	1101000	9,8,7,64,3,2,1	{9,8,64}
105	1101001	9,8,7,64,3,2,1	{9,8,64,1}
106	1101010	9,8,7,64,3,2,1	{9,8,64,2}
107	1101011	9,8,7,64,3,2,1	{9,8,64,2,1}
108	1101100	9,8,7,64,3,2,1	{9,8,64,3}
109	1101101	9,8,7,64,3,2,1	{9,8,64,3,1}
110	1101110	9,8,7,64,3,2,1	{9,8,64,3,2}
111	1101111	9,8,7,64,3,2,1	{9,8,64,3,2,1}
112	1110000	9,8,7,64,3,2,1	{9,8,7}
113	1110001	9,8,7,64,3,2,1	{9,8,7,1}
114	1110010	9,8,7,64,3,2,1	{9,8,7,2}
115	1110011	9,8,7,64,3,2,1	{9,8,7,2,1}
116	1110100	9,8,7,64,3,2,1	{9,8,7,3}
117	1110101	9,8,7,64,3,2,1	{9,8,7,3,1}
118	1110110	9,8,7,64,3,2,1	{9,8,7,3,2}
119	1110111	9,8,7,64,3,2,1	{9,8,7,3,2,1}
120	1111000	9,8,7,64,3,2,1	{9,8,7,64}
121	1111001	9,8,7,64,3,2,1	{9,8,7,64,1}
122	1111010	9,8,7,64,3,2,1	{9,8,7,64,2}
123	1111011	9,8,7,64,3,2,1	{9,8,7,64,2,1}
124	1111100	9,8,7,64,3,2,1	{9,8,7,64,3}
125	1111101	9,8,7,64,3,2,1	{9,8,7,64,3,1}
126	1111110	9,8,7,64,3,2,1	{9,8,7,64,3,2}
127	1111111	9,8,7,64,3,2,1	{9,8,7,64,3,2,1}

List our Power Set P in notation form:

P = {{}, {1}, {2}, {3}, {7}, {8}, {9}, {64}, {2,1}, {3,1}, {3,2}, {64,1}, {64,2}, {64,3}, {7,1}, {7,2}, {7,3}, {7,64}, {8,1}, {8,2}, {8,3}, {8,64}, {8,7}, {9,1}, {9,2}, {9,3}, {9,64}, {9,7}, {9,8}, {3,2,1}, {64,2,1}, {64,3,1}, {64,3,2}, {7,2,1}, {7,3,1}, {7,3,2}, {7,64,1}, {7,64,2}, {7,64,3}, {8,2,1}, {8,3,1}, {8,3,2}, {8,64,1}, {8,64,2}, {8,64,3}, {8,7,1}, {8,7,2}, {8,7,3}, {8,7,64}, {9,2,1}, {9,3,1}, {9,3,2}, {9,64,1}, {9,64,2}, {9,64,3}, {9,7,1}, {9,7,2}, {9,7,3}, {9,7,64}, {9,8,1}, {9,8,2}, {9,8,3}, {9,8,64}, {9,8,7}, {64,3,2,1}, {7,3,2,1}, {7,64,2,1}, {7,64,3,1}, {7,64,3,2}, {8,3,2,1}, {8,64,2,1}, {8,64,3,1}, {8,64,3,2}, {8,7,2,1}, {8,7,3,1}, {8,7,3,2}, {8,7,64,1}, {8,7,64,2}, {8,7,64,3}, {9,3,2,1}, {9,64,2,1}, {9,64,3,1}, {9,64,3,2}, {9,7,2,1}, {9,7,3,1}, {9,7,3,2}, {9,7,64,1}, {9,7,64,2}, {9,7,64,3}, {9,8,2,1}, {9,8,3,1}, {9,8,3,2}, {9,8,64,1}, {9,8,64,2}, {9,8,64,3}, {9,8,7,1}, {9,8,7,2}, {9,8,7,3}, {9,8,7,64}, {7,64,3,2,1}, {8,64,3,2,1}, {8,7,3,2,1}, {8,7,64,2,1}, {8,7,64,3,1}, {8,7,64,3,2}, {9,64,3,2,1}, {9,7,3,2,1}, {9,7,64,2,1}, {9,7,64,3,1}, {9,7,64,3,2}, {9,8,3,2,1}, {9,8,64,2,1}, {9,8,64,3,1}, {9,8,64,3,2}, {9,8,7,2,1}, {9,8,7,3,1}, {9,8,7,3,2}, {9,8,7,64,1}, {9,8,7,64,2}, {9,8,7,64,3}, {8,7,64,3,2,1}, {9,7,64,3,2,1}, {9,8,64,3,2,1}, {9,8,7,3,2,1}, {9,8,7,64,2,1}, {9,8,7,64,3,1}, {9,8,7,64,3,2}, {9,8,7,64,3,2,1}}

Partition 1

{2,1},{9,8,7,64,3}

Partition 2

{2,1},{9,8,7,64,3}

Partition 3

{2,1},{9,8,7,64,3}

Partition 4

{2,1},{9,8,7,64,3}

Partition 5

{2,1},{9,8,7,64,3}

Partition 6

{3,1},

Partition 7

{3,1},

Partition 8

{3,1},

Partition 9

{3,1},

Partition 10

{3,1},

Partition 11

{3,2},

Partition 12

{3,2},

Partition 13

{3,2},

Partition 14

{3,2},

Partition 15

{3,2},

Partition 16

{3,2,1},{9,8,7,64}

Partition 17

{3,2,1},{9,8,7,64}

Partition 18

{3,2,1},{9,8,7,64}

Partition 19

{3,2,1},{9,8,7,64}

Partition 20

{64,1},{9,8,7,64,3}

Partition 21

{64,1},{9,8,7,64,3}

Partition 22

{64,1},{9,8,7,64,3}

Partition 23

{64,1},{9,8,7,64,3}

Partition 24

{64,1},{9,8,7,64,3}

Partition 25

{64,2},{9,8,7,64,3}

Partition 26

{64,2},{9,8,7,64,3}

Partition 27

{64,2},{9,8,7,64,3}

Partition 28

{64,2},{9,8,7,64,3}

Partition 29

{64,2},{9,8,7,64,3}

Partition 30

{64,2,1},

Partition 31

{64,2,1},

Partition 32

{64,2,1},

Partition 33

{64,2,1},

Partition 34

{64,3},

Partition 35

{64,3},

Partition 36

{64,3},

Partition 37

{64,3},

Partition 38

{64,3},

Partition 39

{64,3,1},

Partition 40

{64,3,1},

Partition 41

{64,3,1},

Partition 42

{64,3,1},

Partition 43

{64,3,2},

Partition 44

{64,3,2},

Partition 45

{64,3,2},

Partition 46

{64,3,2},

Partition 47

{64,3,2,1},{9,8,7}

Partition 48

{64,3,2,1},{9,8,7}

Partition 49

{64,3,2,1},{9,8,7}

Partition 50

{7,1},{9,8,7,64,3}

Partition 51

{7,1},{9,8,7,64,3}

Partition 52

{7,1},{9,8,7,64,3}

Partition 53

{7,1},{9,8,7,64,3}

Partition 54

{7,1},{9,8,7,64,3}

Partition 55

{7,2},{9,8,7,64,3}

Partition 56

{7,2},{9,8,7,64,3}

Partition 57

{7,2},{9,8,7,64,3}

Partition 58

{7,2},{9,8,7,64,3}

Partition 59

{7,2},{9,8,7,64,3}

Partition 60

{7,2,1},{9,8,7,64}

Partition 61

{7,2,1},{9,8,7,64}

Partition 62

{7,2,1},{9,8,7,64}

Partition 63

{7,2,1},{9,8,7,64}

Partition 64

{7,3},

Partition 65

{7,3},

Partition 66

{7,3},

Partition 67

{7,3},

Partition 68

{7,3},

Partition 69

{7,3,1},{9,8,7,64}

Partition 70

{7,3,1},{9,8,7,64}

Partition 71

{7,3,1},{9,8,7,64}

Partition 72

{7,3,1},{9,8,7,64}

Partition 73

{7,3,2},{9,8,7,64}

Partition 74

{7,3,2},{9,8,7,64}

Partition 75

{7,3,2},{9,8,7,64}

Partition 76

{7,3,2},{9,8,7,64}

Partition 77

{7,3,2,1},

Partition 78

{7,3,2,1},

Partition 79

{7,3,2,1},

Partition 80

{7,64},{9,8,7,64,3}

Partition 81

{7,64},{9,8,7,64,3}

Partition 82

{7,64},{9,8,7,64,3}

Partition 83

{7,64},{9,8,7,64,3}

Partition 84

{7,64},{9,8,7,64,3}

Partition 85

{7,64,1},

Partition 86

{7,64,1},

Partition 87

{7,64,1},

Partition 88

{7,64,1},

Partition 89

{7,64,2},

Partition 90

{7,64,2},

Partition 91

{7,64,2},

Partition 92

{7,64,2},

Partition 93

{7,64,2,1},

Partition 94

{7,64,2,1},

Partition 95

{7,64,2,1},

Partition 96

{7,64,3},

Partition 97

{7,64,3},

Partition 98

{7,64,3},

Partition 99

{7,64,3},

Partition 100

{7,64,3,1},

Partition 101

{7,64,3,1},

Partition 102

{7,64,3,1},

Partition 103

{7,64,3,2},

Partition 104

{7,64,3,2},

Partition 105

{7,64,3,2},

Partition 106

{7,64,3,2,1},{9,8}

Partition 107

{7,64,3,2,1},{9,8}

Partition 108

{8,1},{9,8,7,64,3}

Partition 109

{8,1},{9,8,7,64,3}

Partition 110

{8,1},{9,8,7,64,3}

Partition 111

{8,1},{9,8,7,64,3}

Partition 112

{8,1},{9,8,7,64,3}

Partition 113

{8,2},{9,8,7,64,3}

Partition 114

{8,2},{9,8,7,64,3}

Partition 115

{8,2},{9,8,7,64,3}

Partition 116

{8,2},{9,8,7,64,3}

Partition 117

{8,2},{9,8,7,64,3}

Partition 118

{8,2,1},{9,8,7,64}

Partition 119

{8,2,1},{9,8,7,64}

Partition 120

{8,2,1},{9,8,7,64}

Partition 121

{8,2,1},{9,8,7,64}

Partition 122

{8,3},

Partition 123

{8,3},

Partition 124

{8,3},

Partition 125

{8,3},

Partition 126

{8,3},

Partition 127

{8,3,1},{9,8,7,64}

Partition 128

{8,3,1},{9,8,7,64}

Partition 129

{8,3,1},{9,8,7,64}

Partition 130

{8,3,1},{9,8,7,64}

Partition 131

{8,3,2},{9,8,7,64}

Partition 132

{8,3,2},{9,8,7,64}

Partition 133

{8,3,2},{9,8,7,64}

Partition 134

{8,3,2},{9,8,7,64}

Partition 135

{8,3,2,1},{9,8,7}

Partition 136

{8,3,2,1},{9,8,7}

Partition 137

{8,3,2,1},{9,8,7}

Partition 138

{8,64},{9,8,7,64,3}

Partition 139

{8,64},{9,8,7,64,3}

Partition 140

{8,64},{9,8,7,64,3}

Partition 141

{8,64},{9,8,7,64,3}

Partition 142

{8,64},{9,8,7,64,3}

Partition 143

{8,64,1},

Partition 144

{8,64,1},

Partition 145

{8,64,1},

Partition 146

{8,64,1},

Partition 147

{8,64,2},

Partition 148

{8,64,2},

Partition 149

{8,64,2},

Partition 150

{8,64,2},

Partition 151

{8,64,2,1},{9,8,7}

Partition 152

{8,64,2,1},{9,8,7}

Partition 153

{8,64,2,1},{9,8,7}

Partition 154

{8,64,3},

Partition 155

{8,64,3},

Partition 156

{8,64,3},

Partition 157

{8,64,3},

Partition 158

{8,64,3,1},{9,8,7}

Partition 159

{8,64,3,1},{9,8,7}

Partition 160

{8,64,3,1},{9,8,7}

Partition 161

{8,64,3,2},{9,8,7}

Partition 162

{8,64,3,2},{9,8,7}

Partition 163

{8,64,3,2},{9,8,7}

Partition 164

{8,64,3,2,1},

Partition 165

{8,64,3,2,1},

Partition 166

{8,7},{9,8,7,64,3}

Partition 167

{8,7},{9,8,7,64,3}

Partition 168

{8,7},{9,8,7,64,3}

Partition 169

{8,7},{9,8,7,64,3}

Partition 170

{8,7},{9,8,7,64,3}

Partition 171

{8,7,1},{9,8,7,64}

Partition 172

{8,7,1},{9,8,7,64}

Partition 173

{8,7,1},{9,8,7,64}

Partition 174

{8,7,1},{9,8,7,64}

Partition 175

{8,7,2},{9,8,7,64}

Partition 176

{8,7,2},{9,8,7,64}

Partition 177

{8,7,2},{9,8,7,64}

Partition 178

{8,7,2},{9,8,7,64}

Partition 179

{8,7,2,1},

Partition 180

{8,7,2,1},

Partition 181

{8,7,2,1},

Partition 182

{8,7,3},{9,8,7,64}

Partition 183

{8,7,3},{9,8,7,64}

Partition 184

{8,7,3},{9,8,7,64}

Partition 185

{8,7,3},{9,8,7,64}

Partition 186

{8,7,3,1},

Partition 187

{8,7,3,1},

Partition 188

{8,7,3,1},

Partition 189

{8,7,3,2},

Partition 190

{8,7,3,2},

Partition 191

{8,7,3,2},

Partition 192

{8,7,3,2,1},

Partition 193

{8,7,3,2,1},

Partition 194

{8,7,64},

Partition 195

{8,7,64},

Partition 196

{8,7,64},

Partition 197

{8,7,64},

Partition 198

{8,7,64,1},

Partition 199

{8,7,64,1},

Partition 200

{8,7,64,1},

Partition 201

{8,7,64,2},

Partition 202

{8,7,64,2},

Partition 203

{8,7,64,2},

Partition 204

{8,7,64,2,1},

Partition 205

{8,7,64,2,1},

Partition 206

{8,7,64,3},

Partition 207

{8,7,64,3},

Partition 208

{8,7,64,3},

Partition 209

{8,7,64,3,1},

Partition 210

{8,7,64,3,1},

Partition 211

{8,7,64,3,2},

Partition 212

{8,7,64,3,2},

Partition 213

{8,7,64,3,2,1},{9}

Partition 214

{9,1},{9,8,7,64,3}

Partition 215

{9,1},{9,8,7,64,3}

Partition 216

{9,1},{9,8,7,64,3}

Partition 217

{9,1},{9,8,7,64,3}

Partition 218

{9,1},{9,8,7,64,3}

Partition 219

{9,2},{9,8,7,64,3}

Partition 220

{9,2},{9,8,7,64,3}

Partition 221

{9,2},{9,8,7,64,3}

Partition 222

{9,2},{9,8,7,64,3}

Partition 223

{9,2},{9,8,7,64,3}

Partition 224

{9,2,1},{9,8,7,64}

Partition 225

{9,2,1},{9,8,7,64}

Partition 226

{9,2,1},{9,8,7,64}

Partition 227

{9,2,1},{9,8,7,64}

Partition 228

{9,3},

Partition 229

{9,3},

Partition 230

{9,3},

Partition 231

{9,3},

Partition 232

{9,3},

Partition 233

{9,3,1},{9,8,7,64}

Partition 234

{9,3,1},{9,8,7,64}

Partition 235

{9,3,1},{9,8,7,64}

Partition 236

{9,3,1},{9,8,7,64}

Partition 237

{9,3,2},{9,8,7,64}

Partition 238

{9,3,2},{9,8,7,64}

Partition 239

{9,3,2},{9,8,7,64}

Partition 240

{9,3,2},{9,8,7,64}

Partition 241

{9,3,2,1},{9,8,7}

Partition 242

{9,3,2,1},{9,8,7}

Partition 243

{9,3,2,1},{9,8,7}

Partition 244

{9,64},{9,8,7,64,3}

Partition 245

{9,64},{9,8,7,64,3}

Partition 246

{9,64},{9,8,7,64,3}

Partition 247

{9,64},{9,8,7,64,3}

Partition 248

{9,64},{9,8,7,64,3}

Partition 249

{9,64,1},

Partition 250

{9,64,1},

Partition 251

{9,64,1},

Partition 252

{9,64,1},

Partition 253

{9,64,2},

Partition 254

{9,64,2},

Partition 255

{9,64,2},

Partition 256

{9,64,2},

Partition 257

{9,64,2,1},{9,8,7}

Partition 258

{9,64,2,1},{9,8,7}

Partition 259

{9,64,2,1},{9,8,7}

Partition 260

{9,64,3},

Partition 261

{9,64,3},

Partition 262

{9,64,3},

Partition 263

{9,64,3},

Partition 264

{9,64,3,1},{9,8,7}

Partition 265

{9,64,3,1},{9,8,7}

Partition 266

{9,64,3,1},{9,8,7}

Partition 267

{9,64,3,2},{9,8,7}

Partition 268

{9,64,3,2},{9,8,7}

Partition 269

{9,64,3,2},{9,8,7}

Partition 270

{9,64,3,2,1},{9,8}

Partition 271

{9,64,3,2,1},{9,8}

Partition 272

{9,7},{9,8,7,64,3}

Partition 273

{9,7},{9,8,7,64,3}

Partition 274

{9,7},{9,8,7,64,3}

Partition 275

{9,7},{9,8,7,64,3}

Partition 276

{9,7},{9,8,7,64,3}

Partition 277

{9,7,1},{9,8,7,64}

Partition 278

{9,7,1},{9,8,7,64}

Partition 279

{9,7,1},{9,8,7,64}

Partition 280

{9,7,1},{9,8,7,64}

Partition 281

{9,7,2},{9,8,7,64}

Partition 282

{9,7,2},{9,8,7,64}

Partition 283

{9,7,2},{9,8,7,64}

Partition 284

{9,7,2},{9,8,7,64}

Partition 285

{9,7,2,1},

Partition 286

{9,7,2,1},

Partition 287

{9,7,2,1},

Partition 288

{9,7,3},{9,8,7,64}

Partition 289

{9,7,3},{9,8,7,64}

Partition 290

{9,7,3},{9,8,7,64}

Partition 291

{9,7,3},{9,8,7,64}

Partition 292

{9,7,3,1},

Partition 293

{9,7,3,1},

Partition 294

{9,7,3,1},

Partition 295

{9,7,3,2},

Partition 296

{9,7,3,2},

Partition 297

{9,7,3,2},

Partition 298

{9,7,3,2,1},{9,8}

Partition 299

{9,7,3,2,1},{9,8}

Partition 300

{9,7,64},

Partition 301

{9,7,64},

Partition 302

{9,7,64},

Partition 303

{9,7,64},

Partition 304

{9,7,64,1},

Partition 305

{9,7,64,1},

Partition 306

{9,7,64,1},

Partition 307

{9,7,64,2},

Partition 308

{9,7,64,2},

Partition 309

{9,7,64,2},

Partition 310

{9,7,64,2,1},{9,8}

Partition 311

{9,7,64,2,1},{9,8}

Partition 312

{9,7,64,3},

Partition 313

{9,7,64,3},

Partition 314

{9,7,64,3},

Partition 315

{9,7,64,3,1},{9,8}

Partition 316

{9,7,64,3,1},{9,8}

Partition 317

{9,7,64,3,2},{9,8}

Partition 318

{9,7,64,3,2},{9,8}

Partition 319

{9,7,64,3,2,1},

Partition 320

{9,8},{9,8,7,64,3}

Partition 321

{9,8},{9,8,7,64,3}

Partition 322

{9,8},{9,8,7,64,3}

Partition 323

{9,8},{9,8,7,64,3}

Partition 324

{9,8},{9,8,7,64,3}

Partition 325

{9,8,1},{9,8,7,64}

Partition 326

{9,8,1},{9,8,7,64}

Partition 327

{9,8,1},{9,8,7,64}

Partition 328

{9,8,1},{9,8,7,64}

Partition 329

{9,8,2},{9,8,7,64}

Partition 330

{9,8,2},{9,8,7,64}

Partition 331

{9,8,2},{9,8,7,64}

Partition 332

{9,8,2},{9,8,7,64}

Partition 333

{9,8,2,1},{9,8,7}

Partition 334

{9,8,2,1},{9,8,7}

Partition 335

{9,8,2,1},{9,8,7}

Partition 336

{9,8,3},{9,8,7,64}

Partition 337

{9,8,3},{9,8,7,64}

Partition 338

{9,8,3},{9,8,7,64}

Partition 339

{9,8,3},{9,8,7,64}

Partition 340

{9,8,3,1},{9,8,7}

Partition 341

{9,8,3,1},{9,8,7}

Partition 342

{9,8,3,1},{9,8,7}

Partition 343

{9,8,3,2},{9,8,7}

Partition 344

{9,8,3,2},{9,8,7}

Partition 345

{9,8,3,2},{9,8,7}

Partition 346

{9,8,3,2,1},

Partition 347

{9,8,3,2,1},

Partition 348

{9,8,64},

Partition 349

{9,8,64},

Partition 350

{9,8,64},

Partition 351

{9,8,64},

Partition 352

{9,8,64,1},{9,8,7}

Partition 353

{9,8,64,1},{9,8,7}

Partition 354

{9,8,64,1},{9,8,7}

Partition 355

{9,8,64,2},{9,8,7}

Partition 356

{9,8,64,2},{9,8,7}

Partition 357

{9,8,64,2},{9,8,7}

Partition 358

{9,8,64,2,1},

Partition 359

{9,8,64,2,1},

Partition 360

{9,8,64,3},{9,8,7}

Partition 361

{9,8,64,3},{9,8,7}

Partition 362

{9,8,64,3},{9,8,7}

Partition 363

{9,8,64,3,1},

Partition 364

{9,8,64,3,1},

Partition 365

{9,8,64,3,2},

Partition 366

{9,8,64,3,2},

Partition 367

{9,8,64,3,2,1},

Partition 368

{9,8,7},{9,8,7,64}

Partition 369

{9,8,7},{9,8,7,64}

Partition 370

{9,8,7},{9,8,7,64}

Partition 371

{9,8,7},{9,8,7,64}

Partition 372

{9,8,7,1},

Partition 373

{9,8,7,1},

Partition 374

{9,8,7,1},

Partition 375

{9,8,7,2},

Partition 376

{9,8,7,2},

Partition 377

{9,8,7,2},

Partition 378

{9,8,7,2,1},

Partition 379

{9,8,7,2,1},

Partition 380

{9,8,7,3},

Partition 381

{9,8,7,3},

Partition 382

{9,8,7,3},

Partition 383

{9,8,7,3,1},

Partition 384

{9,8,7,3,1},

Partition 385

{9,8,7,3,2},

Partition 386

{9,8,7,3,2},

Partition 387

{9,8,7,3,2,1},

Partition 388

{9,8,7,64},

Partition 389

{9,8,7,64},

Partition 390

{9,8,7,64},

Partition 391

{9,8,7,64,1},

Partition 392

{9,8,7,64,1},

Partition 393

{9,8,7,64,2},

Partition 394

{9,8,7,64,2},

Partition 395

{9,8,7,64,2,1},

Partition 396

{9,8,7,64,3},

Partition 397

{9,8,7,64,3},

Partition 398

{9,8,7,64,3,1},

Partition 399

{9,8,7,64,3,2},

Partition 400

{{9},{8},{7},{64},{3},{2},{1})

Treat this as a Vector

(a₁, a₂, a₃, a₄, a₅, a₆, a₇) = (1, 2, 3, 7, 8, 9, 64)

Calculate the magnitude:

||A|| = Square Root(a₁² + a₂² + a₃² + a₄² + a₅² + a₆² + a₇²)
||A|| = Square Root(1² + 2² + 3² + 7² + 8² + 9² + 64²)
||A|| = √1 + 4 + 9 + 49 + 64 + 81 + 4096
||A|| = √4304
||A|| = 65.604877867427

Treat this as a sequence

Find the explicit formula and terms

Not a series

The series you entered was neither an arithmetic nor geometric series.
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