You entered a number set X of {17,26,42,59}
From the 4 numbers you entered, we want to calculate the mean, variance, standard deviation, standard error of the mean, skewness, average deviation (mean absolute deviation), median, mode, range, Pearsons Skewness Coefficient of that number set, entropy, midrange
17, 26, 42, 59
59, 42, 26, 17
Sort our number set in ascending order
and assign a ranking to each number:
Number Set Value  17  26  42  59 
Rank  1  2  3  4 
Since we have 4 numbers in our original number set,
we assign ranks from lowest to highest (1 to 4)
Our original number set in unsorted order was 17,26,42,59
Our respective ranked data set is 1,2,3,4
Root Mean Square =  √A 
√N 
where A = x_{1}^{2} + x_{2}^{2} + x_{3}^{2} + x_{4}^{2} and N = 4 number set items
A = 17^{2} + 26^{2} + 42^{2} + 59^{2}
A = 289 + 676 + 1764 + 3481
A = 6210
RMS =  √6210 
√4 
RMS =  78.803553219382 
2 
RMS = 39.401776609691
Central tendency contains:
Mean, median, mode, harmonic mean,
geometric mean, midrange, weightedaverage:
μ =  Sum of your number Set 
Total Numbers Entered 
μ =  ΣX_{i} 
n 
μ =  17 + 26 + 42 + 59 
4 
μ =  144 
4 
μ = 36
Since our number set contains 4 elements which is an even number,
our median number is determined as follows
Number Set = (n_{1},n_{2},n_{3},n_{4})
Median Number 1 = ½(n)
Median Number 1 = ½(4)
Median Number 1 = Number Set Entry 2
Median Number 2 = Median Number 1 + 1
Median Number 2 = Number Set Entry 2 + 1
Median Number 2 = Number Set Entry 3
Median = ½(n_{2} + n_{3})
Our median is the average of entry 2 and entry 3 of our number set highlighted in red:
(17,26,42,59)
Median = ½(26 + 42)
Median = ½(68)
Median = 34
The highest frequency of occurence in our number set is 1 times
by the following numbers in green:
()
Since the maximum frequency of any number is 1, no mode exists.
Mode = N/A
Harmonic Mean =  N 
1/x_{1} + 1/x_{2} + 1/x_{3} + 1/x_{4} 
With N = 4 and each x_{i} a member of the number set you entered, we have:
Harmonic Mean =  4 
1/17 + 1/26 + 1/42 + 1/59 
Harmonic Mean =  4 
0.058823529411765 + 0.038461538461538 + 0.023809523809524 + 0.016949152542373 
Harmonic Mean =  4 
0.1380437442252 
Harmonic Mean = 28.976322124924
Geometric Mean = (x_{1} * x_{2} * x_{3} * x_{4})^{1/N}
Geometric Mean = (17 * 26 * 42 * 59)^{1/4}
Geometric Mean = 1095276^{0.25}
Geometric Mean = 32.35049221287
MidRange =  Maximum Value in Number Set + Minimum Value in Number Set 
2 
MidRange =  59 + 17 
2 
MidRange =  76 
2 
MidRange = 38
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
{59,42,26,17}
Stem  Leaf 

5  9 
4  2 
2  6 
1  7 
Mean, Variance, Standard Deviation, Median, Mode
μ =  Sum of your number Set 
Total Numbers Entered 
μ =  ΣX_{i} 
n 
μ =  17 + 26 + 42 + 59 
4 
μ =  144 
4 
μ = 36
Let's evaluate the square difference from the mean of each term (X_{i}  μ)^{2}:
(X_{1}  μ)^{2} = (17  36)^{2} = 19^{2} = 361
(X_{2}  μ)^{2} = (26  36)^{2} = 10^{2} = 100
(X_{3}  μ)^{2} = (42  36)^{2} = 6^{2} = 36
(X_{4}  μ)^{2} = (59  36)^{2} = 23^{2} = 529
ΣE(X_{i}  μ)^{2} = 361 + 100 + 36 + 529
ΣE(X_{i}  μ)^{2} = 1026
Population  Sample  


 

 
Variance: σ_{p}^{2} = 256.5  Variance: σ_{s}^{2} = 342  
Standard Deviation: σ_{p} = √σ_{p}^{2} = √256.5  Standard Deviation: σ_{s} = √σ_{s}^{2} = √342  
Standard Deviation: σ_{p} = 16.0156  Standard Deviation: σ_{s} = 18.4932 
Population  Sample  


 

 

 
SEM = 8.0078  SEM = 9.2466 
Skewness =  E(X_{i}  μ)^{3} 
(n  1)σ^{3} 
Let's evaluate the square difference from the mean of each term (X_{i}  μ)^{3}:
(X_{1}  μ)^{3} = (17  36)^{3} = 19^{3} = 6859
(X_{2}  μ)^{3} = (26  36)^{3} = 10^{3} = 1000
(X_{3}  μ)^{3} = (42  36)^{3} = 6^{3} = 216
(X_{4}  μ)^{3} = (59  36)^{3} = 23^{3} = 12167
ΣE(X_{i}  μ)^{3} = 6859 + 1000 + 216 + 12167
ΣE(X_{i}  μ)^{3} = 4524
Skewness =  E(X_{i}  μ)^{3} 
(n  1)σ^{3} 
Skewness =  4524 
(4  1)16.0156^{3} 
Skewness =  4524 
(3)4107.9924850764 
Skewness =  4524 
12323.977455229 
Skewness = 0.36708927912558
AD =  ΣX_{i}  μ 
n 
Evaluate the absolute value of the difference from the mean
X_{i}  μ:
X_{1}  μ = 17  36 = 19 = 19
X_{2}  μ = 26  36 = 10 = 10
X_{3}  μ = 42  36 = 6 = 6
X_{4}  μ = 59  36 = 23 = 23
ΣX_{i}  μ = 19 + 10 + 6 + 23
ΣX_{i}  μ = 58
Calculate average deviation (mean absolute deviation)
AD =  ΣX_{i}  μ 
n 
AD =  58 
4 
Average Deviation = 14.5
Since our number set contains 4 elements which is an even number,
our median number is determined as follows
Number Set = (n_{1},n_{2},n_{3},n_{4})
Median Number 1 = ½(n)
Median Number 1 = ½(4)
Median Number 1 = Number Set Entry 2
Median Number 2 = Median Number 1 + 1
Median Number 2 = Number Set Entry 2 + 1
Median Number 2 = Number Set Entry 3
Median = ½(n_{2} + n_{3})
Our median is the average of entry 2 and entry 3 of our number set highlighted in red:
(17,26,42,59)
Median = ½(26 + 42)
Median = ½(68)
Median = 34
The highest frequency of occurence in our number set is 1 times
by the following numbers in green:
()
Since the maximum frequency of any number is 1, no mode exists.
Mode = N/A
Range = Largest Number in the Number Set  Smallest Number in the Number Set
Range = 59  17
Range = 42
PSC1 =  μ  Mode 
σ 
PSC1 =  3(36  N/A) 
16.0156 
Since no mode exists, we do not have a Pearsons Skewness Coefficient 1
PSC2 =  μ  Median 
σ 
PSC1 =  3(36  34) 
16.0156 
PSC2 =  3 x 2 
16.0156 
PSC2 =  6 
16.0156 
PSC2 = 0.3746
Entropy = Ln(n)
Entropy = Ln(4)
Entropy = 1.3862943611199
MidRange =  Smallest Number in the Set + Largest Number in the Set 
2 
MidRange =  59 + 17 
2 
MidRange =  76 
2 
MidRange = 38
We need to sort our number set from lowest to highest shown below:
{17,26,42,59}
V =  y(n + 1) 
100 
V =  75(4 + 1) 
100 
V =  75(5) 
100 
V =  375 
100 
V = 3 ← Rounded down to the nearest integer
Upper quartile (UQ) point = Point # 3 in the dataset which is 42
17,26,42,59V =  y(n + 1) 
100 
V =  25(4 + 1) 
100 
V =  25(5) 
100 
V =  125 
100 
V = 1 ← Rounded up to the nearest integer
Lower quartile (LQ) point = Point # 1 in the dataset which is 17
17,26,42,59
IQR = UQ  LQ
IQR = 42  17
IQR = 25
Lower Inner Fence (LIF) = LQ  1.5 x IQR
Lower Inner Fence (LIF) = 17  1.5 x 25
Lower Inner Fence (LIF) = 17  37.5
Lower Inner Fence (LIF) = 20.5
Upper Inner Fence (UIF) = UQ + 1.5 x IQR
Upper Inner Fence (UIF) = 42 + 1.5 x 25
Upper Inner Fence (UIF) = 42 + 37.5
Upper Inner Fence (UIF) = 79.5
Lower Outer Fence (LOF) = LQ  3 x IQR
Lower Outer Fence (LOF) = 17  3 x 25
Lower Outer Fence (LOF) = 17  75
Lower Outer Fence (LOF) = 58
Upper Outer Fence (UOF) = UQ + 3 x IQR
Upper Outer Fence (UOF) = 42 + 3 x 25
Upper Outer Fence (UOF) = 42 + 75
Upper Outer Fence (UOF) = 117
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 58 < v < 20.5 and 79.5 < v < 117
17,26,42,59
Highly Suspect Outliers are values outside the outer fences
We wish to mark all values in our dataset (v) in red below such that v < 58 or v > 117
17,26,42,59
Array
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 =  
n 
Weighted Average =  
0 
Weighted Average =  
0 
Weighted Average =  0 
0 
Weighted Average = NAN
Show the freqency distribution table for this number set
17, 26, 42, 59
We need to choose the smallest integer k such that 2^{k} ≥ n where n = 0
Therefore, we use 0 intervals
Our maximum value in our number set of 59  17 = 42
Each interval size is the difference of the maximum and minimum value divided by the number of intervals
Interval Size =  42 
0 
Add 1 to this giving us INF + 1 = INF
Class Limits  Class Boundaries  FD  CFD  RFD  CRFD 

0  100% 
Go through our 4 numbers
Determine the ratio of each number to the next one
17:26 → 0.6538
26:42 → 0.619
42:59 → 0.7119
Successive Ratio = 17:26,26:42,42:59 or 0.6538,0.619,0.7119