Pdf

Woek 2 g <2 Sproag angd Shape Agenda Shape Qua £ Milos, 5 Numbg, Q Spread 1QR SUmmary ang Box Plotg opulation Standard Deviation ')lunplu Standard Deviation Shapo of o Distribution Describj . p ibing Shape (of o Data Distribution) - Statisticiang use the wordy below (o describe the shape of a data distribution !"t 'v""' A VL PR Jl'fiylnd.;lné pets positively skewed of skewed to the right 1[ '1 " e Al symmetric and bel) shaped negatively skewed or skewed to the left uniform af Quartiles Quart_iles are the values that divide a data set into 4 equal parts. The median is the 2nd quartile, Q2. The 1st quartile, Q1, is the median of the lower half of the data. The 3rd Quartile, Q3, is the median of the upper half of the data. To find quartiles: ' 1. Place the data in order from 11/ o gid # b Find the median of the data o " Find the median of the lower half of the data. » . Find the median of the upper half of the data. o 2, 3. 4. ! Example 1: Find the minimum, Q1, Q2, Q3, and maximum of the data set: 22, 43,14, 7.2, 32, 9,38, 12. We call this finding the five number summary of a data set. -d

Spread or Variation The Interquartile Range (IQR) is the difference b calculate the IQR = - Stwveen i i lay of y, OESDNENS Dyl L - e A - N7 The bax contains the middie 50% of the datg and vig The right ssgment displays the top 25% of the datg ™ of the data. A dox plot makes it easy to see whe ° N a a '\ Example 2 Data Setis % e ERN a. Find the S Number Summary: ¢ Whatpercentofthe dataislessthan 7 | *° ? €. \What percent of the data is greater than * ? —_— Either the vaniance or the standard deviation can be used to represent the spreag if the data § reasonably and has no strong s o ) _—— . Population Variance is the av erage of the square distances to the mean. _ \ i Population Variance Formula: W. -

\ | J \\ Example 3: Find the population variance and population standard deviation of 10, 12, 14, 16, 18 Step 1: The Mean is: Step 2: The distances to the mean are: Step 3: The square distances to the mean are: ' Step 4: The sum of the square distances to the mean: : i r mean square distance: . | ST o : root of the variance: ] e i : jati are o Step 6: The Standard Dewanc')'r: ?'r s?L_l o s' £ I L Step 1: Population Mean p = ' ' - : dph W (> = ey' ¥ w1l 0 ¥ (09 0t ¥4 [ ew Il et L i L I \$ ¥4 g-4 =4 K oyt = b ¥] 3«\{? U G AT 7'("'[1(' |4 q 4 (1 L{ ol [ 1{@/ Step 5: Population Variance fr o= U0 o g ( "i/ - 7 [}/fi Step 6: Population Standard Deviation A \ - —~ '// ). 74 /) \ 0 N VAL ¥ | -~ J A * - IS W IIWT S L Bl P TTame ] TR UV T TOWORE T SPOATI R v mEETY