You entered a number set X of {2,4,6,8,10}
From the 5 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,
midrangeCalculate Mean denoted as μμ =  Sum of your number Set 
 Total Numbers Entered 
μ = 6Calculate Variance denoted as σ^{2}Let's evaluate the square difference from the mean of each term (X
_{i}  μ)
^{2}:
(X
_{1}  μ)
^{2} = (2  6)
^{2} = 4
^{2} = 16
(X
_{2}  μ)
^{2} = (4  6)
^{2} = 2
^{2} = 4
(X
_{3}  μ)
^{2} = (6  6)
^{2} = 0
^{2} = 0
(X
_{4}  μ)
^{2} = (8  6)
^{2} = 2
^{2} = 4
(X
_{5}  μ)
^{2} = (10  6)
^{2} = 4
^{2} = 16
Adding our 5 sum of squared differences up, we have our variance numerator: ΣE(X
_{i}  μ)
^{2} = 16 + 4 + 0 + 4 + 16
ΣE(X
_{i}  μ)
^{2} = 40
Now that we have the sum of squared differences from the means, calculate variance:Population  Sample 

σ^{2} =  ΣE(X_{i}  μ)^{2}   n 
 σ^{2} =  ΣE(X_{i}  μ)^{2}   n  1 



Variance: σ_{p}^{2} = 8  Variance: σ_{s}^{2} = 10 
Standard Deviation: σ_{p} = √σ_{p}^{2} = √8  Standard Deviation: σ_{s} = √σ_{s}^{2} = √10 
Standard Deviation: σ_{p} = 2.8284  Standard Deviation: σ_{s} = 3.1623 
Calculate the Standard Error of the Mean:Calculate Skewness: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} = (2  6)
^{3} = 4
^{3} = 64
(X
_{2}  μ)
^{3} = (4  6)
^{3} = 2
^{3} = 8
(X
_{3}  μ)
^{3} = (6  6)
^{3} = 0
^{3} = 0
(X
_{4}  μ)
^{3} = (8  6)
^{3} = 2
^{3} = 8
(X
_{5}  μ)
^{3} = (10  6)
^{3} = 4
^{3} = 64
Adding our 5 sum of cubed differences up, we have our skewness numerator: ΣE(X
_{i}  μ)
^{3} = 64 + 8 + 0 + 8 + 64
ΣE(X
_{i}  μ)
^{3} = 0
Now that we have the sum of cubed differences from the means, calculate skewness:Skewness =  E(X_{i}  μ)^{3} 
 (n  1)σ^{3} 
Skewness =  0 
 (5  1)2.8284^{3} 
Skewness = 0Calculate Average Deviation (Mean Absolute Deviation) denoted below:Let's evaluate the absolute value of the difference from the mean of each term X
_{i}  μ:
X
_{1}  μ = 2  6 = 4 = 4
X
_{2}  μ = 4  6 = 2 = 2
X
_{3}  μ = 6  6 = 0 = 0
X
_{4}  μ = 8  6 = 2 = 2
X
_{5}  μ = 10  6 = 4 = 4
Adding our 5 absolute value of differences from the mean, we have our average deviation numerator: ΣX
_{i}  μ = 4 + 2 + 0 + 2 + 4
ΣX
_{i}  μ = 12
Now that we have the absolute value of the differences from the means, calculate average deviation (mean absolute deviation):Average Deviation = 2.4 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 = (n
_{1},n
_{2},n
_{3},n
_{4},n
_{5})
Median Number = Entry ½(n + 1)
Median Number = Entry ½(6)
Median Number = n
_{3}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 = 6Calculate 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.
Mode = N/ACalculate the RangeRange = Largest Number in the Number Set  Smallest Number in the Number Set
Range = 10  2
Range =
8Calculate Pearsons Skewness Coefficient 1:Since no mode exists, we do not have a Pearsons Skewness Coefficient 1
Calculate Pearsons Skewness Coefficient 2:PSC2 =
0Calculate Entropy:Entropy = Ln(n)
Entropy = Ln(5)
Entropy =
1Calculate MidRange:MidRange =  Smallest Number in the Set + Largest Number in the Set 
 2 
MidRange =
6