## 1. Mean, SD and SEM, etc ##
(2019-12-23, 5:39pm)

 

Data = 1, 2, 2.1, 2.9, 3, 3.1, 4, 3.9, 5

 

[Mean, SD and SEM]
   Arithmetic Mean = 3.0
   SD(n) = 1.1372482 (Standard Deviation)
   SD(n-1) = 1.2062339 (Standard Deviation)
   SEM = 0.40207794
            (Standard error of the mean)
   n = 9

 

[Confidence Interval (CI)]
   95% CI : 2.0728076 --- 3.9271924
         t(8, 0.05) = 2.3060
   99% CI : 1.6508832 --- 4.349117
         t(8, 0.01) = 3.3554

 

[Skewness and Kurtosis]

 

   ### > See [Help]

 

   Skewness (g1) = 0.0
         (Excel: SKEW.P function)
   Skewness (G1) = 0.0
         (Excel: SKEW function)
   Kurtosis (α4 (= g2 + 3) ) = 2.345653
   Kurtosis (g2) = -0.6543469
   Kurtosis (G2) = -0.103517905
         (Excel: KURT function)

 

[Others]
   Sum = 27.0 (Sum of Data)
   SS = 11.64 (Sum of Squares)

 

   V(n) = 1.2933333 (Variance)
   V(n-1) = 1.455 (Unbiased variance)

 

   SD(n) = 1.1372482
         (SD of sample group.
         Excel: STDEV.P function)
   SD(n-1) = 1.2062339
         (SD as estimate for population.
         Excel: STDEV function)

 

   %CV = 37.90827

 

[Various Means]
   Arithmetic Mean = 3.0
   Geometric mean = 2.744539
   Harmonic mean = 2.443433