Frequency distribution, histogram, and statistics

Type or paste the data:

Max data to display:

    

N or n:      ∑xi:      ∑x2:    RMS=:

Measures/statistics of central tendancy/location/middle/center/typical/representative:
    Mean or μ:      Median ̃x:     Mode: uni: bi:     Midrange:

    Trimmed mean: 5%(each end):     10%:

Measures/statistics of dispersion/variation/spread/scatter/uncertainty/volatility:
   Range:
   Standard deviation SD s:    σN:

   Data is "statistically significant" if it is less than -2s= or greater than +2s=

   Variance VAR σ2: s2:     

   Standard error SEM=s/√n:

   Sample coefficient of variation, CV=s/x̄*100:

   MAD (mean [absolute] deviation): MADσ  Normal:

5-number summary:
Min:    Q1:    Q2:    Q3:    Max:      IQR:

Outliers:
  Data ≤ Q1-1.5*IQR=
  
  Data ≥ Q3+1.5*IQR=
  

Hildebrand H=(-̃x)/s: If |H|<.2, symmetric. H>.2 right skewed, H<-.2 left skewed    
Skew: |skew|<.5 symmetric, between .5 and 1 moderately skewed, >1 highly skewed.    
(Excess) Kurtosis: "tailedness"

Empirical Rule and Chebyshev
% of the data within
1 SD of mean (x̄±s):
2 SDs of mean (x̄±2s):
3 SDs of mean (x̄±3s):

Sorted data:

Freq. distr.        Datums      Freq.  Cuml.freq. Rel. freq. Cuml.rel.freq
    

#uniques=

Histogram: (yellow curve is ogive)

X min: X max: Y max: Class size/width:

Binned frequency distribution:
Class start Freq.     Cuml.freq. Rel.freq. Cuml.Rel.freq.   Norm Expected*n Normquant Z's
                 
                 (Freqs as Oi, Norm Expecteds as Ei into Χ2 GOF)


Z scores: σn-1

Z scores: σn


Normal quantile plot's expected Z scores from a normally distributed sample:

Copy and paste these as the Y values in the Correlation_Regression webpage to see the normal quantile plot. Use the above Sorted data values as the corresponding X values.