DESCRIPTIVE STATISTICS: GROUPED DATA Confidence Level 95.000%
Strength of Concrete             Significance Level 5.0%   Grouped data for histogram from Cusens and Wettern, 1959, in Alfredo H-S. Ang and Wilson H. Tang, Probability Concepts in Engineering Planning and Design, Vol. 1 ( New York, NY: John Wiley & Sons, 1975), pp. 276-277.
t(α/2,n-1) 1.976810963
Observations Group Limits
Number of Observations 143 Minimum 6
Number of Groups 8 Maximum 10
Optimal Number of Groups [Sturges' Rule] 8.159871337 Range 4
Interval Midpoint Group Frequencies
Mean 7.479895105 Minimum 7
Median 7.439516129 Maximum 31
Mode 7.4375 Range 24
Geometric Mean 7.456757423
Harmonic Mean 7.434333272
Population Sample
Population Standard Deviation 0.598959316 Sample Standard Deviation 0.601064627
Population Variance 0.358752262 Sample Variance 0.361278686
Coefficient of Variation 0.080075898 Coefficient of Variation 12.00029342
Standard Error of the Mean 0.050087494 Standard Error of the Mean 0.050263549
95% Confidence Interval for Population Mean 95% Confidence Interval for Sample Mean
Lower Limit L 7.380881597 Lower Limit L 7.38053357
Upper Limit U 7.578908613 Upper Limit U 7.57925664
Quartiles, Deciles, Percentiles 95% Confidence Interval for Population Mean Symmetry Quartiles, Deciles, Percentiles
Skewness 0.889485942 Lowest Q0 D0 P0 6
Standard Error of Skewness (SES) 0.202731198   P1 6.119166667
Skewness Test Statistic (Skewness/SES) 4.387513874   P5 6.595833333
Distribution's Deviation from Symmetry Extended to Right   D1 P10 6.827941176
Peakedness Q1   P25 7.110795455
Kurtosis 4.80472287 Median Q2 D5 P50 7.439516129
Standard Error of Kurtosis (SEK) 0.402792267 Q3   P75 7.753125
Excess Kurtosis 1.80472287   D9 P90 8.094444444
Kurtosis Test Statistic (Excess Kurtosis/SEK) 4.480530084   P95 8.491666667
Shape of Distribution's Peak Leptokurtic   P99 9.693571429
Distribution's Degree of Peakedness Near Normal Highest Q4 D10 P100 10
Inter-Quartile Range Q3-Q1 0.642329545
Correlation
Correlation (Pearson) CORR(τ,O) -0.28943636
Population Moments
Bar Lengths as % of Maximum
m1 -9.93766E-17
m2 0.358752262 Confidence Inteval for Mean 100%
m3 0.191130968 Percentiles 15%
m4 0.618383138 Mode 100%
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