You entered a number set X of {30,50,70,30}
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
30, 30, 50, 70
Rank Ascending
30 is the 1st lowest/smallest number
30 is the 2nd lowest/smallest number
50 is the 3rd lowest/smallest number
70 is the 4th lowest/smallest number
70, 50, 30, 30
Rank Descending
70 is the 1st highest/largest number
50 is the 2nd highest/largest number
30 is the 3rd highest/largest number
30 is the 4th highest/largest number
Sort our number set in ascending order
and assign a ranking to each number:
Number Set Value  30  30  50  70 
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 30,30,50,70
Our respective ranked data set is 2,2,3,4
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 = 30^{2} + 30^{2} + 50^{2} + 70^{2}
A = 900 + 900 + 2500 + 4900
A = 9200
RMS =  √9200 
√4 
RMS =  95.916630466254 
2 
RMS = 47.958315233127
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 =  30 + 30 + 50 + 70 
4 
μ =  180 
4 
μ = 45
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:
(30,30,50,70)
Median = ½(30 + 50)
Median = ½(80)
Median = 40
The highest frequency of occurence in our number set is 2 times
by the following numbers in green:
()
Our mode is denoted as: 30
Mode = 30
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 
1/30 + 1/30 + 1/50 + 1/70 
Harmonic Mean =  4 
0.033333333333333 + 0.033333333333333 + 0.02 + 0.014285714285714 
Harmonic Mean =  4 
0.10095238095238 
Harmonic Mean = 39.622641509434
Geometric Mean = (x_{1} * x_{2} * x_{3} * x_{4})^{1/N}
Geometric Mean = (30 * 30 * 50 * 70)^{1/4}
Geometric Mean = 3150000^{0.25}
Geometric Mean = 42.128659306105
MidRange =  Maximum Value in Number Set + Minimum Value in Number Set 
2 
MidRange =  70 + 30 
2 
MidRange =  100 
2 
MidRange = 50
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
{70,50,30,30}
Stem  Leaf 

7  0 
5  0 
3  0,0 
Mean, Variance, Standard Deviation, Median, Mode
μ =  Sum of your number Set 
Total Numbers Entered 
μ =  ΣX_{i} 
n 
μ =  30 + 30 + 50 + 70 
4 
μ =  180 
4 
μ = 45
Let's evaluate the square difference from the mean of each term (X_{i}  μ)^{2}:
(X_{1}  μ)^{2} = (30  45)^{2} = 15^{2} = 225
(X_{2}  μ)^{2} = (30  45)^{2} = 15^{2} = 225
(X_{3}  μ)^{2} = (50  45)^{2} = 5^{2} = 25
(X_{4}  μ)^{2} = (70  45)^{2} = 25^{2} = 625
ΣE(X_{i}  μ)^{2} = 225 + 225 + 25 + 625
ΣE(X_{i}  μ)^{2} = 1100
Population  Sample  


 

 
Variance: σ_{p}^{2} = 275  Variance: σ_{s}^{2} = 366.66666666667  
Standard Deviation: σ_{p} = √σ_{p}^{2} = √275  Standard Deviation: σ_{s} = √σ_{s}^{2} = √366.66666666667  
Standard Deviation: σ_{p} = 16.5831  Standard Deviation: σ_{s} = 19.1485 
Population  Sample  


 

 

 
SEM = 8.2916  SEM = 9.5743 
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} = (30  45)^{3} = 15^{3} = 3375
(X_{2}  μ)^{3} = (30  45)^{3} = 15^{3} = 3375
(X_{3}  μ)^{3} = (50  45)^{3} = 5^{3} = 125
(X_{4}  μ)^{3} = (70  45)^{3} = 25^{3} = 15625
ΣE(X_{i}  μ)^{3} = 3375 + 3375 + 125 + 15625
ΣE(X_{i}  μ)^{3} = 9000
Skewness =  E(X_{i}  μ)^{3} 
(n  1)σ^{3} 
Skewness =  9000 
(4  1)16.5831^{3} 
Skewness =  9000 
(3)4560.3393265512 
Skewness =  9000 
13681.017979654 
Skewness = 0.65784578409186
AD =  ΣX_{i}  μ 
n 
Evaluate the absolute value of the difference from the mean
X_{i}  μ:
X_{1}  μ = 30  45 = 15 = 15
X_{2}  μ = 30  45 = 15 = 15
X_{3}  μ = 50  45 = 5 = 5
X_{4}  μ = 70  45 = 25 = 25
ΣX_{i}  μ = 15 + 15 + 5 + 25
ΣX_{i}  μ = 60
Calculate average deviation (mean absolute deviation)
AD =  ΣX_{i}  μ 
n 
AD =  60 
4 
Average Deviation = 15
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:
(30,30,50,70)
Median = ½(30 + 50)
Median = ½(80)
Median = 40
The highest frequency of occurence in our number set is 2 times
by the following numbers in green:
()
Our mode is denoted as: 30
Mode = 30
Range = Largest Number in the Number Set  Smallest Number in the Number Set
Range = 70  30
Range = 40
PSC1 =  μ  Mode 
σ 
PSC1 =  3(45  30) 
16.5831 
PSC1 =  3 x 15 
16.5831 
PSC1 =  45 
16.5831 
PSC1 = 2.7136
PSC2 =  μ  Median 
σ 
PSC1 =  3(45  40) 
16.5831 
PSC2 =  3 x 5 
16.5831 
PSC2 =  15 
16.5831 
PSC2 = 0.9045
Entropy = Ln(n)
Entropy = Ln(4)
Entropy = 1.3862943611199
MidRange =  Smallest Number in the Set + Largest Number in the Set 
2 
MidRange =  70 + 30 
2 
MidRange =  100 
2 
MidRange = 50
We need to sort our number set from lowest to highest shown below:
{30,30,50,70}
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 50
30,30,50,70V =  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 30
30,30,50,70
IQR = UQ  LQ
IQR = 50  30
IQR = 20
Lower Inner Fence (LIF) = LQ  1.5 x IQR
Lower Inner Fence (LIF) = 30  1.5 x 20
Lower Inner Fence (LIF) = 30  30
Lower Inner Fence (LIF) = 0
Upper Inner Fence (UIF) = UQ + 1.5 x IQR
Upper Inner Fence (UIF) = 50 + 1.5 x 20
Upper Inner Fence (UIF) = 50 + 30
Upper Inner Fence (UIF) = 80
Lower Outer Fence (LOF) = LQ  3 x IQR
Lower Outer Fence (LOF) = 30  3 x 20
Lower Outer Fence (LOF) = 30  60
Lower Outer Fence (LOF) = 30
Upper Outer Fence (UOF) = UQ + 3 x IQR
Upper Outer Fence (UOF) = 50 + 3 x 20
Upper Outer Fence (UOF) = 50 + 60
Upper Outer Fence (UOF) = 110
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 30 < v < 0 and 80 < v < 110
30,30,50,70
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 < 30 or v > 110
30,30,50,70
30, 30, 50, 70
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 =  X_{1}p_{1} + X_{2}p_{2} + X_{3}p_{3} + X_{4}p_{4} 
n 
Weighted Average =  30 x 0.2 + 30 x 0.4 + 50 x 0.6 + 70 x 0.8 
4 
Weighted Average =  6 + 12 + 30 + 56 
4 
Weighted Average =  104 
4 
Weighted Average = 26
Show the freqency distribution table for this number set
30, 30, 50, 70
We need to choose the smallest integer k such that 2^{k} ≥ n where n = 4
For k = 1, we have 2^{1} = 2
For k = 2, we have 2^{2} = 4 ← Use this since it is greater than our n value of 4
Therefore, we use 2 intervals
Our maximum value in our number set of 70  30 = 40
Each interval size is the difference of the maximum and minimum value divided by the number of intervals
Interval Size =  40 
2 
Add 1 to this giving us 20 + 1 = 21
Class Limits  Class Boundaries  FD  CFD  RFD  CRFD 

30  51  29.5  51.5  3  3  3/4 = 75%  3/4 = 75% 
51  72  50.5  72.5  1  3 + 1 = 4  1/4 = 25%  4/4 = 100% 
4  100% 
Go through our 4 numbers
Determine the ratio of each number to the next one
30:30 → 1
30:50 → 0.6
50:70 → 0.7143
Successive Ratio = 30:30,30:50,50:70 or 1,0.6,0.7143