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5 5 5 4 5 6 4 5 6 4 5 6 3 4 5 6 7 3 4 5 6 7 3 4 5 6 7 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 3 6 9 6 3 0 0 0 0 0 0 0 0 0 0 0 0.1111 0.2222 0.3333 0.2222 0.1111 0 0 0 0 0 0 0 0 0 0.11111 0.22222 0.33333 0.22222 0.11111 5 5 5 4 5 6 4 5 6 4 5 6 3 4 5 6 7 3 4 5 6 7 3 4 5 6 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 SAMPLE STEM PLOT 0 POPULATION PARAMET 0 mean 5 0 3 3 median 5 0 4 4 mode 5 0 5 5 5 variance 1.3333 0 6 6 st.dev. 1.1547 0 0 0 SAMPLE STATISTICS 1 mean 4.5556 1 median 5 1 mode 5 1 variance 1.2778 1 st.dev 1.1304 1 The probability of a Sample L 1 1 1 Probability of this Sample =
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1 2 2 The probability of the most lik The probability of the least lik PROB possible values sample values 1 2 3 4 5 6 7 8 9 10 11 12 13 14 5 0.333 0 0 0 0 1 0 0 0 0 0 0 0 0 0 5 0.333 0 0 0 0 1 0 0 0 0 0 0 0 0 0 6 0.222 0 0 0 0 0 1 0 0 0 0 0 0 0 0 3 0.111 0 0 1 0 0 0 0 0 0 0 0 0 0 0 4 0.222 0 0 0 1 0 0 0 0 0 0 0 0 0 0 3 0.111 0 0 1 0 0 0 0 0 0 0 0 0 0 0 6 0.222 0 0 0 0 0 1 0 0 0 0 0 0 0 0 5 0.333 0 0 0 0 1 0 0 0 0 0 0 0 0 0 4 0.222 0 0 0 1 0 0 0 0 0 0 0 0 0 0
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Total 27 <------ STEM PLOT: CAN INPUT NUMBERS IN THE YELLOW CELLS 1 1 1 2 2 1 2 3 0 0 0 0 0 counts 27 6.7722E+012 1 1 6 0 0 0 0 0 probabilities 1.38645E-018 1 1 0.00137 9E-006 17 18 19 20 21 TERS ( SAMPLE SIZE = 9 ) A NEW SAMPLE WILL BE DRAWN EACH TIME "DEL" KEY IS PRES WHEN THE CURSOR IS IN AN EMPTY CELL. 2 0 0 2 Like This Pattern… * p1 p2 p3 Prob.Prod. 1.115E-006 1 1 0.01235 Combination 7560 factorial 1 1 2 0.00843 or 3265920 times as likely as the least likely sample
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15120 1 1 1 kely sample among them is 0.01685982 <--- approximately 0 0 1 kely sample among them is 2.5811748E-009 0 0 0.11111 1.11507E-006 1 1 0.11111 15 16 17 18 19 20 21 1 2 3 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.11111 0 0 0 0 0 0 0 0 0 0 0 0.22222 0 0 0 0 0 0 0 0 0 0.11111 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.22222
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BUT SO AS TO FORM A STEM PLOT. 4 5 6 7 8 9 10 11 12 13 14 720 362880 720 6 1 1 1 1 1 1 1 0.00012 5E-005 0.00012 0.00137 1 1 1 1 1 1 1 SSED 2 3 2 2 3 2 0 0 0 0 0 0 0 0 p4 p5 p6 p7 p8 p9 p10 p11 p12 p13 p14 0.04938 0.03704 0.04938 1 1 1 1 1 1 1 1 2 6 2 1 1 1 1 1 1 1 1
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2 6 2 1 1 1 1 1 1 1 1 2 3 2 1 0 0 0 0 0 0 0 0.22222 0.33333 0.22222 0.11111 0 0 0 0 0 0 0 0.04938 0.03704 0.04938 0.11111 1 1 1 1 1 1 1 5 6 7 8 9 10 11 12 13 14 15 0.33333 0 0 0 0 0 0 0 0 0 0 0.33333 0 0 0 0 0 0 0 0 0 0 0 0.22222 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.22222 0 0 0 0 0 0 0 0 0 0.33333 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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15 16 17 18 19 20 21 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 p15 p16 p17 p18 p19 p20 p21 1 1 1 1 1 1 1 1 1 1 1 1 1 1
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1 1 1 1 1 1 1 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 1 1 1 1 1 1 1 16 17 18 19 20 21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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5 5 5 4 5 6 4 5 6 4 5 6 3 4 5 6 7 3 4 5 6 7 3 4 5 6 7 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 3 6 9 6 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0.111111 0.22 0.33 0.22 0.11 0 0 0 0 0 0 0 0 0 0 0 5 5 5 4 5 6 4 5 6 4 5 6 3 4 5 6 7 3 4 5 6 7 3 4 5 6 7 SAMPLE STEM PLOT (WITHOUT REPLACEMENT) AFTER 12 DRAWS POPULATION PARAMETERS 0 mean 5 0 median 5 0 mode 5 5 5 5 0 4 4 4 variance 1.3333333 0 5 5 5 st.dev. 1.1547005 0 6 6 6 6 6 1 0 7 0 SAMPLE STATISTICS 0 mean 5.3333333 1 median 5.5 1 mode 6 6 6 6 1 variance 0.969697 1 st.dev 0.9847319 1 1 1 1 1 1
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2 2 Calculate the probability of the sample = 0.2727 out of 17383860 1 0.2222 58 or 15689 out of 10^12 or 1 trillion 2 0.1923 87 3 0.16 116 The number of possible sample of size 4 0.125 145 out of a total of 27 objects is …………… 5 0.2609 174 Thus the probability of a given sample without 6 0.2273 203 looking into its properties is 1 over 7 0.4286 232 8 0.2 261 9 0.1579 290 10 0.4444 319 11 0.1176 348 12 0.4375 377
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total 27 <----- SAME STEM PLOT AS IN THE PREVIOUS TAB. IF THE OTHER ONE CHANGES, IT WILL 1 2 2 0 0 0 count THE 12 WITHOUT REPLACEMENT DRA 0 0 0 frequencies 10 9 18 8 17 7 16 6 9 15 24 5 8 14 23 4 7 13 22 3 3 6 12 21 27 2 2 5 11 20 26 1 1 4 10 19 25 0 0 0.111 0.222 0.333 0.222 0.111 0 0 0 0 3 6 9 6 3 0 0 5 5 5 draw 6 1 10 9 12 8 11 7 10 6 3 9 18 5 2 8 17 6
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