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statistica
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source: D.C. Montgomery - Applied Statistics and Probability for Engineers
pb.4
562 869 708 775 775 704 809
856 655 806 878 909 918 558
768 870 918 940 946 661 820
898 935 952 957 693 835 905
939 955 960 498 653 730 753
(a) Compute the sample mean, variance, and standard deviation.
(b) Find the sample upper and lower quartiles.
(c) Find the sample median.
(d) Construct a box plot of the data.
(e) Find the 5th and 95th percentiles.
c) calculati mediana; d) trasati graficul tip box-plot; e) gasiti percentilele 5 si 95
a) calculati media, variatia si deviatia standard; b) gasiti cuartila superioara si cea inferioara
Construct a cumulative frequency plot and histogram for the solar intensity data. Use
6 bins
Calculate the sample mean and sample standard deviation. Prepare a dot diagram of
these data. Indicate where the sample mean falls on this diagram. Provide a practical
interpretation of the sample mean.
The following data are direct solar intensity measurements on different
days at a location in southern Spain:
Date reprezinta masuratori ale intensitatii razelor solare in diferite zile intr-o zona din
sudul Spaniei.
Calculati media si deviatia standard. Trasati diagrama prin puncte ale acestor valori.
Indicati unde este apare media pe aceste grafic. Oferiti o interpretare practica a mediei
Trasati histograma valorilor intensitatii solare si diagrama fercventelor cumulate. Folosind
6, respectiv 12 bin-uri
min 498
max 960
amplitude 462
1st quartile 719
3rd quartile 918
sample mean 810,51
standard deviation 128,32
variance 15995,2
median 835
mode 775
490 590 690 790 890 990
dot diagram of direct solar intensity measurements
Cumulative frequency Bin Frequency This table use Data Analysis from Data menu
490 0490 0 570 3 490-570570 3 650 0 570-650650 3 730 7 650-730730 10 810 6 730-810810 16 890 6 810-890890 22 970 13 890-970970 35 More 0
Input range: C5:I9
Frequencies
Activate first Data Analysis option from Excel options (File menu ) -> Add-Ins -> select Analysis Toolpak -> the press Go
After that should be appear in Data Analysis in Data menu
Use now Data -> Data Analysis -> Histogram
Bin Range: O5:O11Output range: select area for display results
before finish your command press keyCtrl+Shift+EnterThis will become an array function
0
0,0005
0,001
0,0015
0,002
0,0025
0,003
0,0035
505
525
545
565
585
605
625
645
665
685
705
725
745
765
785
805
825
845
865
885
905
925
945
965
985
Probability mass function
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
150
552
554
556
558
560
562
564
566
568
570
572
574
576
578
580
582
584
586
588
590
592
594
596
598
5
Cumulative distribution function
0
2
4
6
8
10
12
14
490-570 570-650 650-730 730-810 810-890 890-970
frequency
490 0,006248251 0,000137351
495 0,006969353 0,000151277
500 0,007762953 0,000166362
505 0,008635013 0,000182673
510 0,009591838 0,000200279
515 0,010640074 0,000219249
520 0,011786712 0,000239651
525 0,013039086 0,000261555
530 0,014404873 0,000285027
535 0,015892083 0,000310135
540 0,017509054 0,000336942
545 0,019264441 0,000365511
550 0,021167203 0,000395901
555 0,023226583 0,000428168
560 0,025452091 0,000462361
565 0,027853481 0,000498527
570 0,030440722 0,000536707
575 0,033223968 0,000576935
580 0,036213528 0,000619236
585 0,039419822 0,000663631
590 0,042853347 0,00071013
595 0,04652463 0,000758734
600 0,05044418 0,000809434
605 0,054622436 0,000862213
610 0,059069719 0,000917039
615 0,063796169 0,000973872
620 0,06881169 0,001032657
625 0,074125888 0,00109333
630 0,079748009 0,001155812
635 0,085686871 0,001220011
640 0,091950803 0,001285821
645 0,098547575 0,001353126
650 0,105484334 0,001421793
655 0,112767537 0,001491678
660 0,120402887 0,001562625
665 0,128395268 0,001634461
670 0,136748682 0,001707007
675 0,145466195 0,001780068
680 0,154549876 0,001853439
685 0,164000747 0,001926907
690 0,173818734 0,002000248
x
Cumulative
distribution function
Probability mass
function
=NORMDIST(P15;$M
$12;$M$13;TRUE)
=NORMDIST(P15;$
M$12;$M$13;
FALSE)
695 0,184002626 0,00207323
700 0,194550035 0,002145614
705 0,205457366 0,002217157
710 0,21671979 0,00228761
715 0,228331226 0,00235672
720 0,24028433 0,002424235
725 0,25257049 0,0024899
730 0,265179828 0,002553464
735 0,278101214 0,002614678
740 0,291322284 0,002673298
745 0,304829468 0,002729084
750 0,318608023 0,002781809
755 0,332642081 0,002831249
760 0,346914695 0,002877197
765 0,361407901 0,002919454
770 0,376102782 0,002957838
775 0,390979544 0,00299218
780 0,40601759 0,003022328
785 0,42119561 0,003048148
790 0,436491666 0,003069525
795 0,451883294 0,003086362
800 0,467347595 0,003098584
805 0,482861344 0,003106134
810 0,498401088 0,003108978
815 0,51394326 0,003107104
820 0,529464277 0,00310052
825 0,544940657 0,003089256
830 0,560349118 0,003073363
835 0,575666686 0,003052912
840 0,590870798 0,003027997
845 0,605939402 0,002998729
850 0,62085105 0,002965238
855 0,635584991 0,002927673
860 0,65012126 0,002886198
865 0,664440753 0,002840994
870 0,678525304 0,002792255
875 0,692357752 0,002740188
880 0,705922003 0,002685013
885 0,719203079 0,002626957
890 0,732187164 0,002566257
895 0,744861645 0,002503156
900 0,757215136 0,002437902
905 0,769237499 0,002370747
910 0,780919863 0,002301945
915 0,792254622 0,002231748
920 0,803235436 0,002160409
925 0,81385722 0,002088177
930 0,824116127 0,002015298
935 0,834009523 0,001942012
940 0,843535958 0,001868552
945 0,852695126 0,001795143
950 0,86148783 0,001722001
955 0,869915926 0,001649333
960 0,87798228 0,001577335
965 0,885690705 0,001506192
970 0,89304591 0,001436075
975 0,900053433 0,001367145
980 0,906719583 0,001299549
985 0,91305137 0,001233421
990 0,91905644 0,001168882
995 0,924743014 0,001106039
1000 0,930119814 0,001044987
skewness -0,75223 Skewness: indicator used in distribution analysis as a sign of asymmetry and deviation from a normal distribution.
kurtosis -0,29608 Interpretation:
Skewness = 0 - mean = median, the distribution is symmetrical around the mean.
Kurtosis - indicator used in distribution analysis as a sign of flattening or "peakedness" of a distribution.
Interpretation:
Kurtosis = 3 - Mesokurtic distribution - normal distribution for example.
Kurtosis < 3 - Platykurtic distribution, flatter than a normal distribution with a wider peak. The probability for extreme values is
less than for a normal distribution, and the values are wider spread around the mean.
Skewness > 0 - Right skewed distribution - most values are concentrated on left of the mean, with extreme values to the right.
Skewness < 0 - Left skewed distribution - most values are concentrated on the right of the mean, with extreme values to the
left.
Kurtosis > 3 - Leptokurtic distribution, sharper than a normal distribution, with values concentrated around the mean and
thicker tails. This means high probability for extreme values.