frequency_distributions

frequency_distributions - Describing Data Describing...

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Unformatted text preview: Describing Data Describing Frequency Distributions and Frequency Graphs Graphs Finding Limits… Finding Real Real limits of a number: midway point between the number & the next lower and next higher number on the scale next 35.5 60/1 36.5 upper limit lower real limit 15 45 35 30 36 37 36 seconds Let’s say the mean was 36.21… Let’s 36.205 36.215 36.20 36.21 36.22 What are Frequency Distributions? What Table Table that orders scores from highest to lowest. Also tells you how often each score occurred score Necker Cube Necker Mach Pyramid Mach Time seen as pyramid – raw scores Time (measured in seconds) X 18 2 7 23 16 10 5 30 5 15 X 17 3 31 9 11 10 1 13 5 8 X 19 16 2 14 4 7 7 6 2 10 X 6 26 8 24 7 19 7 11 9 4 X 7 6 1 3 5 13 3 8 9 7 Frequency Distributions Frequency 10-20 class intervals (10) = # of cat XLargest = 31 XSmallest = 1 31 Largest Smallest L- S L# of cat = 31-1 10 = 30 10 = 3.0 Size of the interval Class Interval Real Limits Class Lower Upper Midpoint Lower 30-32 30-32 9-11 9-11 6-8 3-5 0-2 5.5 2.5 -.5 8.5 5.5 2.5 7 4 1 Group Frequency Distribution Group Class Real Limits Mid- tally freq Class Interval lower upper point Interval 30-32 30-32 27-29 24-26 21-23 18-20 15-17 12-14 9-11 6-8 3-5 0-2 29.5 32.5 26.5 29.5 23.5 26.5 20.5 23.5 17.5 20.5 14.5 17.5 11.5 14.5 8.5 11.5 5.5 8.5 2.5 5.5 -.5 2.5 31 II 2 28 0 25 II 2 22 I 1 19 III 3 16 IIII 4 13 III 3 10 IIII III 8 7 IIII IIII III 13 4 IIII IIII 9 1 IIII 5 rf .04 0 .04 .02 .06 .08 .06 .16 .26 .18 .10 %f 4 0 4 2 6 8 6 16 26 18 10 cf crf 50 1.00 48 .96 48 .96 46 .92 45 .90 42 .84 38 .76 35 .70 27 .54 14 .28 5 .10 Histogram -.5 1 4 7 10 13 16 19 22 25 28 31 Time (sec) Frequency Polygon -.5 1 4 7 10 13 16 19 Time (sec) 22 25 28 31 Simple Bar Graph Simple Used Cat for qualitative variables Show Participation Breed Frequency Breed Persian 6 Persian Siamese 4 Siamese Angora 5 Angora American Shorthair 5 American 6 5 Frequency 4 3 2 1 0 Persian Siamese Angora American Shorthair Stem and Leaf Plots Stem Combo of frequency table and histogram Uses 1s, 10s, 100s digits to sort and Uses group group Mach pyramid data write numbers 01 to 09 10 to 19 20 to 29 digits Tens30 to 39 Ones digit Could Stem and Leaf Plots Stem Stem 3 2 1 0 5, 9, Leaf 0,1 3, 4, 6 0, 0, 1, 1, 3, 3, 4, 5, 6, 7, 8, 9 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 1, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 9, 9 9, More Detailed Stem and Leaf Plots More Break each 10s digit into halves: 0-4 & 5-9 Mach pyramid data A more detailed stem and leaf plot more Stem Leaf 3* ° 0, 1 2* 6 ° 3, 4 1 * 5, 6, 7, 8, 9 ° 0, 0, 1, 1, 3, 3, 4 0 * 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 9 ° 1, 1, 2, 2, 2, 3, 3, 3, 4, 4 Shapes of Distributions Shapes Can be symmetrical or asymmetrical Skewed distribution Scores are clustered at one end Positively Positively skewed if the TAIL, NOT THE SCORES, occur at high end occur Negatively skewed if the TAIL, NOT THE Negatively SCORES, occur at low end SCORES, Modality Most frequently occurring score Normal Distribution Normal Positively Skewed Positively Negatively Skewed Negatively ...
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