Descriptive statistics relative to the data


Discuss the below:

1) Can you kindly explain what the confidence % truly means at the bottom of the descriptive statistics relative to the data?

2) How would I determine if the accuracy of the data would improve if there were more data points? In other words, can the number of data points somehow determine the confidence interval for the data????

3) How would I determine whether the data columns represent a normal or log normal distribution? How do I produce a distribution diagram or curve?

4) How would I produce a probability graph for any column of data ---- i.e. plotting concentration of the compound on the x-axis and probability on the y-axis ---- how is this done? We are supposed to understand the significance of outlier data here?

5) How do I determine the percentile ranking of the data? In other words, how do I determine what percentile the data points lie within?

6) I've seen confidence intervals described by what looks like a box & whisker plot ----- but how would I determine or plot the confidence intervals and then determine the upper and lower control limits based on the data?

7) How can or does the confidence interval for a data set improve?? What has to happen to the data for the CI to improve? And what bearing does the outlier data have?

Data set

















Date Cadmium Chromium Lead Mercury Ash Content Chlorine Heat Content S.G.
Sampled mg/kg mg/kg mg/kg mg/kg % mg/kg BTU/lb  
24-Mar-09 0.05 0.127 0.25 0.040 0.0168 5.0   0.7996
5-Jun-09 0.05 0.242 0.25 0.004 0.3387 5.0 15165 0.8390
8-Sep-09 0.10 0.250 0.50 0.004 0.0145 5.0   0.8314
2-Dec-09 0.20 0.500 1.00 0.004 0.0103 5.0   0.8336
12-Mar-10 0.10 0.250 0.50 0.020 0.0314 5.0 17554 0.8050
18-Jun-10 0.10 0.250 0.50 0.020 0.0145 5.0   0.8362
1-Sep-10 0.10 0.250 0.50 0.020 0.0400 5.0 14100 0.8140
6-Dec-10 0.10 0.250 0.50 0.020 0.0100 5.0 16700 0.8085
28-Mar-11 0.10 0.250 0.50 0.020 0.0100 5.0 15000 0.8172
7-Jun-11 0.10 0.500 0.50 0.020 0.0100 5.0 16300 0.8285
29-Jun-11 0.10 0.250 0.50 0.020 0.0200 5.0 15100 0.8245
1-Sep-11 0.10 0.250 0.50 0.020 0.0500 11.0 12900 0.8768
8-Dec-11 0.10 0.250 0.50 0.020 0.1000 5.0 14500 0.8832
5-Mar-12 0.10 0.250 0.50 0.020 0.0300 10.0 13500 0.8800
14-Jun-12 0.10 0.468 0.50 0.020 0.0300 10.0 13700 0.8885
5-Sep-12 0.10 0.250 0.50 0.020 0.0400 10.0 14300 0.8949
4-Dec-12 0.10 0.250 0.50 0.020 0.0230 15.0 15900 0.8395
6-Mar-13 0.10 0.250 0.50 0.020 0.0360 15.0 14100 0.8641
2-Jun-13 0.10 0.250 0.50 0.020 0.0220 9.1 14700 0.8730
2-Sep-13 0.10 0.349 0.50 0.020 0.0190 29.8 15500 0.8537
2-Dec-13 0.10 0.250 0.50 0.020 0.0910 25.4 16800 0.8607
9-Mar-14 0.10 0.250 0.50 0.020 0.0880 5.0 13000 0.8280









Mean 0.1 0.281182 0.5 0.018727 0.04750909 9.104545 14934.38889 0.844541
Standard Error 0.005698 0.019525 0.02849 0.001566 0.01498563 1.462644 313.9598153 0.006192
Median 0.1 0.25 0.5 0.02 0.0265 5 14850 0.8376
Mode 0.1 0.25 0.5 0.02 0.01 5 14100 #N/A
Standard Deviation 0.026726 0.091581 0.133631 0.007343 0.07028885 6.860409 1332.018686 0.029041
Sample Variance 0.000714 0.008387 0.017857 5.39E-05 0.00494052 47.06522 1774273.781 0.000843
Kurtosis 10.5 2.293972 10.5 4.063022 15.2665262 3.963119 -0.62406259 -1.16985
Skewness 2.057912 1.607819 2.057912 0.010706 3.70772641 2.062043 0.325290291 0.245128
Range 0.15 0.373 0.75 0.036 0.3287 24.8 4654 0.0953
Minimum 0.05 0.127 0.25 0.004 0.01 5 12900 0.7996
Maximum 0.2 0.5 1 0.04 0.3387 29.8 17554 0.8949
Sum 2.2 6.186 11 0.412 1.0452 200.3 268819 18.5799
Count 22 22 22 22 22 22 18 22
Largest(1) Kth 0.2 0.5 1 0.04 0.3387 29.8 17554 0.8949
Smallest(1) Kth 0.05 0.127 0.25 0.004 0.01 5 12900 0.7996
Confidence Level(95.0%) 0.01185 0.040605 0.059248 0.003256 0.03116433 3.041735 662.3973031 0.012876

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Basic Statistics: Descriptive statistics relative to the data
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