Descriptive Statistics Slides

  • Published on
    26-Dec-2014

  • View
    13

  • Download
    0

Embed Size (px)

Transcript

<p>... " "</p> <p> 1 ( ) , squash, badminton . &lt; 30 30-50 &gt; 50 7 1 9 10 4 0 20 11 4 5 10 27 4 1 18 33</p> <p>... " "</p> <p> 2 . .i 1 0 - 2.5 2 2.5 - 5.0 3 5.0 - 7.5 4 7.5 - 10 5 10 fi 201 372 260 80 10 Fi 201 573 833 913 923 F i /n 0.218 0.621 0.902 0.989 1.000</p> <p>... " "</p> <p> 1. (Pies) 2. 3. </p> <p>A B</p> <p>fi 19 16</p> <p>f i /n 0.543 0.457</p> <p>A B</p> <p>... " "</p> <p> 1. (Pies) 2. 3. fi 19 16 f i /n 0.543 0.4570.560 0.540 0.520 0.500 0.480 0.460 0.440 0.420 0.400 A B</p> <p>A B</p> <p>... " "</p> <p> 1. (Pies) 2. 3. 0-9 110 - 19 20 - 29 30 - 39 40 - 49 50 - 59 fi 5 11 20 9 13 7 f i /n% 7.7% 16.9% 30.8% 13.8% 20.0% 10.8%25</p> <p>20</p> <p>15</p> <p>10</p> <p>5</p> <p>0 0 -- 9 10 -- 19 20 -- 29 30 -- 39 40 -- 49 50 -- 59</p> <p>... " "</p> <p> 1. (Pies) 2. 3. ( ) 0-9 110 - 19 20 - 29 30 - 39 40 - 49 50 - 59 fi 5 11 20 9 13 7 f i /n% 7.7% 16.9% 30.8% 13.8% 20.0% 10.8%25 20 15 10 5 0 0 -- 9 10 -- 19 20 -- 29 30 -- 39 40 -- 49 50 -- 59</p> <p>... " "</p> <p> 1. (Pies) 2. 3. () 0-9 110 - 19 20 - 29 30 - 39 40 - 49 50 - 59 fi 5 11 20 9 13 7 f i /n% 7.7% 16.9% 30.8% 13.8% 20.0% 10.8%25 20 15 10 5 0 0 -- 9</p> <p>10 -- 19</p> <p>20 -- 29</p> <p>30 -- 39</p> <p>40 -- 49</p> <p>50 -- 59</p> <p>... " "</p> <p> - - 0.4 0.3 0.2</p> <p>0.1</p> <p> 1 2</p> <p>-2</p> <p>-1</p> <p>0.12 0.1 0.08 0.06 0.04 0.02 2 4 6 8 10 12 14</p> <p>x</p> <p> ( &lt; m &lt; x )x</p> <p>0.8</p> <p>0.6</p> <p>0.4</p> <p>0.2</p> <p> ( &gt; m &gt; x )0.2 0.4 0.6 0.8 1 1.2</p> <p>... " "</p> <p> (Percentiles) , 100 p% 100 (1-p)% .</p> <p>... " "</p> <p> (Percentiles)1. 2. 3. 4. (quartile) Q1 75% Q3 25% (Q2) k (n + 1) (Dk) 10 </p> <p> n +1 4 </p> <p> 3( n + 1) 4 </p> <p>5. (Pk)</p> <p> k (n + 1) 100 </p> <p>... " "</p> <p> (Percentiles) 1 4, 6, 7, 15, 18, 20, 25 n= 7, 7 +1 Q1 = 6 =2 4 3(7 + 1) = 6 Q3 = 20 4</p> <p>... " "</p> <p> (Percentiles) 2 n= 8, 4, 6, 7, 15, 18, 20, 23, 25 Q1 = 6.25( 2 25% 3 .)</p> <p>8 +1 = 2.25 4</p> <p>3(8 + 1) = 6.75 4</p> <p>Q3 = 22.25 ( 6 </p> <p> 75% 7 .)</p> <p>... " "</p> <p> q qn , , Fi-1 &lt; q n Fi i- :</p> <p>hi P = ai 1 + ( qn Fi 1 ) fi... " "</p> <p> 0-5 15 - 10 110 - 20 20 - 35 35 - 60 60 -100 fi 3 7 16 18 12 4 f i /h i 0,6 1,4 1,6 1,2 0,8 0,1 Fi 3 10 26 44 56 60</p> <p> , Q3 , d7 , P5 .</p> <p>Q2 = m , q = Q2 = 20 +15 18</p> <p>1 2</p> <p>, qn=</p> <p>1 2</p> <p>60 = 30</p> <p>(30 - 26) = 23.33</p> <p>hi P = ai 1 + ( qn Fi 1 ) fi... " "</p> <p> 0-5 15 - 10 110 - 20 20 - 35 35 - 60 60 -100 fi 3 7 16 18 12 4 f i /h i 0,6 1,4 1,6 1,2 0,8 0,1 Fi 3 10 26 44 56 60</p> <p> , Q3 , d7 , P5 .</p> <p>q=</p> <p>3 4</p> <p>, qn=25 12</p> <p>3 4</p> <p>60 = 45</p> <p>Q3 = 35 +</p> <p>(45 - 44) = 37.08</p> <p>hi P = ai 1 + ( qn Fi 1 ) fi... " "</p> <p> 0-5 15 - 10 110 - 20 20 - 35 35 - 60 60 -100 fi 3 7 16 18 12 4 f i /h i 0,6 1,4 1,6 1,2 0,8 0,1 Fi 3 10 26 44 56 60</p> <p> , Q3 , d7 , P5 .</p> <p>q=</p> <p>7 10</p> <p>, qn=15 18</p> <p>7 10</p> <p>60 = 42</p> <p>d7 = 20 +</p> <p>(42 - 26) = 33.3</p> <p>hi P = ai 1 + ( qn Fi 1 ) fi... " "</p> <p> 0-5 15 - 10 110 - 20 20 - 35 35 - 60 60 -100 fi 3 7 16 18 12 4 f i /h i 0,6 1,4 1,6 1,2 0,8 0,15 100</p> <p>Fi 3 10 26 44 56 60</p> <p> , Q3 , d7 , P5 .</p> <p>q=</p> <p>5 100</p> <p>, qn=5 3</p> <p>60 = 3</p> <p>P5 = 0 +</p> <p>(3 - 0) = 5</p> <p>hi P = ai 1 + ( qn Fi 1 ) fi... " "</p> <p> (skewness) 1 n ( xi x )3 ' m3 n i =1 g1 = = 3 3 ' 2 n (m2 ) 1 ( x x )2 2 i n i =1 </p> <p>0.12</p> <p>0.1 0.08 0.06 0.04 0.02 2 4 6 8 10 12 14</p> <p> g1&gt; 0 </p> <p>0.8</p> <p>0.6</p> <p>x</p> <p>0.4</p> <p> g1&lt; 0 1 1.2</p> <p>0.2</p> <p>0.2</p> <p>0.4</p> <p>0.6</p> <p>0.8</p> <p>... " "</p> <p> (Kurtosis)g2 =0.4</p> <p>(m )</p> <p>' m4</p> <p>' 2 2</p> <p>3=</p> <p>1 n ( xi x )4 n i =1 1 ( xi x )2 n i =1 n 2</p> <p>3</p> <p>0.3</p> <p>0.2</p> <p>0.1</p> <p> g2 . (outliers)2 4</p> <p>-4</p> <p>-2</p> <p>0.4</p> <p>0.3</p> <p>0.2</p> <p>0.1</p> <p> g2 .2 4</p> <p>-4</p> <p>-2</p> <p>... " "</p> <p>Box Plots-100 2 4 6 8 12 15 13 25 23 36 35 38 34 29 9 10 30 27 100 42 38 53 -23 -33 -15 -16 -17 -9 -4 -5 5 -11 -3 -2 95 92 -60 33 -33Statistics var Mean Median Variance Skewness Kurtosis Minimum Maximum Percentiles 25 50 75 12.08 9.50 1,428.328 -0.080 1.898 -100 100 -8.00 9.50 33.75</p> <p>... " "</p> <p>Box Plots-100 2 4 6 8 12 15 13 25 23 36 35 38 34 29 9 10 30 27 100 42 38 53 -23 -33 -15 -16 -17 -9 -4 -5 5 -11 -3 -2 95 92 -60 33 -33100A A</p> <p>50</p> <p>var</p> <p>0</p> <p>-50</p> <p>-100</p> <p>A</p> <p>... " "</p>